56:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000 Números reales:@0.073089:0.043661:0.211864:0.043661:0.211864:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b. Esta ecuación tiene la forma . En este caso, el término está multiplicando a:@0.293660:0.136836:0.927012:0.136836:0.927012:0.120402:0.293660:0.120402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ax:@0.532618:0.136836:0.549258:0.136836:0.549258:0.120430:0.532618:0.120430:0.000000:0.000000 5:@0.553473:0.136281:0.568807:0.136281:0.568807:0.122566:0.553473:0.122566:0.000000 b:@0.572985:0.136836:0.582244:0.136836:0.582244:0.120430:0.572985:0.120430:0.000000 a:@0.765635:0.136836:0.774894:0.136836:0.774894:0.120430:0.765635:0.120430:0.000000 la incógnita. Por lo tanto, debe pasar al segundo miembro a dividir.:@0.323769:0.153478:0.806643:0.153478:0.806643:0.137044:0.323769:0.137044:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4 20; :@0.323769:0.184376:0.418197:0.184378:0.418197:0.167944:0.323769:0.167943:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.332678:0.184376:0.340133:0.184376:0.340133:0.167970:0.332678:0.167970:0.000000 5 2:@0.344017:0.183822:0.378549:0.183822:0.378549:0.170106:0.344017:0.170106:0.000000:0.000000:0.000000 x:@0.474386:0.184378:0.481841:0.184378:0.481841:0.167972:0.474386:0.167972:0.000000 :@0.481767:0.184378:0.504997:0.184378:0.504997:0.167944:0.481767:0.167944:0.000000:0.000000:0.000000 5 2:@0.485725:0.183823:0.520257:0.183823:0.520257:0.170107:0.485725:0.170107:0.000000:0.000000:0.000000 20:@0.522529:0.179161:0.540403:0.179161:0.540403:0.162727:0.522529:0.162727:0.000000:0.000000 4:@0.526984:0.193140:0.535967:0.193140:0.535967:0.176706:0.526984:0.176706:0.000000 ;:@0.542697:0.184378:0.545900:0.184378:0.545900:0.167944:0.542697:0.167944:0.000000 x:@0.655112:0.184378:0.662567:0.184378:0.662567:0.167972:0.655112:0.167972:0.000000 5:@0.662493:0.184378:0.709873:0.184378:0.709873:0.167944:0.662493:0.167944:0.000000:0.000000:0.000000:0.000000:0.000000 5 2:@0.666451:0.183823:0.700983:0.183823:0.700983:0.170107:0.666451:0.170107:0.000000:0.000000:0.000000 c.:@0.293660:0.211741:0.304797:0.211741:0.304797:0.195307:0.293660:0.195307:0.000000:0.000000 Esta ecuación tiene la forma . En este caso, primero pasamos el término:@0.323861:0.211741:0.926883:0.211741:0.926883:0.195307:0.323861:0.195307:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ax:@0.533513:0.211741:0.550171:0.211741:0.550171:0.195335:0.533513:0.195335:0.000000:0.000000 1 5:@0.554486:0.211186:0.603007:0.211186:0.603007:0.197470:0.554486:0.197470:0.000000:0.000000:0.000000 b:@0.574108:0.211741:0.583367:0.211741:0.583367:0.195335:0.574108:0.195335:0.000000 c:@0.607296:0.211741:0.614954:0.211741:0.614954:0.195335:0.607296:0.195335:0.000000 que no tiene la incógnita al segundo miembro, para luego pasar el término que:@0.323769:0.228383:0.926743:0.228383:0.926743:0.211949:0.323769:0.211949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 multiplica a la incógnita, así::@0.323769:0.245025:0.525874:0.245025:0.525874:0.228591:0.323769:0.228591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3 6 21; :@0.323769:0.275923:0.424201:0.275923:0.424201:0.259489:0.323769:0.259489:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.332678:0.275923:0.340133:0.275923:0.340133:0.259517:0.332678:0.259517:0.000000 2 5:@0.344017:0.275368:0.391398:0.275368:0.391398:0.261652:0.344017:0.261652:0.000000:0.000000:0.000000 3 21 6; :@0.474379:0.275923:0.574799:0.275923:0.574799:0.259489:0.474379:0.259489:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.483288:0.275923:0.490743:0.275923:0.490743:0.259517:0.483288:0.259517:0.000000 5:@0.494627:0.275368:0.509960:0.275368:0.509960:0.261652:0.494627:0.261652:0.000000 1:@0.535565:0.275368:0.550898:0.275368:0.550898:0.261652:0.535565:0.261652:0.000000 3 27; :@0.594863:0.275923:0.659288:0.275923:0.659288:0.259489:0.594863:0.259489:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.603772:0.275923:0.611227:0.275923:0.611227:0.259517:0.603772:0.259517:0.000000 5:@0.615111:0.275368:0.630444:0.275368:0.630444:0.261652:0.615111:0.261652:0.000000 :@0.715357:0.275923:0.749916:0.275923:0.749916:0.259489:0.715357:0.259489:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.719304:0.275923:0.726759:0.275923:0.726759:0.259517:0.719304:0.259517:0.000000 5:@0.730643:0.275368:0.745977:0.275368:0.745977:0.261652:0.730643:0.261652:0.000000 27:@0.752207:0.270707:0.770080:0.270707:0.770080:0.254273:0.752207:0.254273:0.000000:0.000000 3:@0.756661:0.284686:0.765644:0.284686:0.765644:0.268252:0.756661:0.268252:0.000000 ;:@0.772374:0.275923:0.775577:0.275923:0.775577:0.259489:0.772374:0.259489:0.000000 x:@0.839788:0.275923:0.847243:0.275923:0.847243:0.259517:0.839788:0.259517:0.000000 9:@0.847170:0.275923:0.879309:0.275923:0.879309:0.259489:0.847170:0.259489:0.000000:0.000000:0.000000:0.000000 5:@0.851127:0.275368:0.866460:0.275368:0.866460:0.261652:0.851127:0.261652:0.000000 Ejemplo 2:@0.293663:0.303285:0.369446:0.303285:0.369446:0.286615:0.293663:0.286615:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Resuelve la ecuación ( 3) ( 2) 6 ( 1) 17:@0.293663:0.330647:0.708054:0.330649:0.708054:0.314215:0.293663:0.314213:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.453015:0.330647:0.460470:0.330647:0.460470:0.314241:0.453015:0.314241:0.000000 2:@0.464354:0.330092:0.479687:0.330092:0.479687:0.316376:0.464354:0.316376:0.000000 x:@0.505991:0.330647:0.513446:0.330647:0.513446:0.314241:0.505991:0.314241:0.000000 1:@0.517330:0.330092:0.532663:0.330092:0.532663:0.316376:0.517330:0.316376:0.000000 2:@0.554163:0.330092:0.569496:0.330092:0.569496:0.316376:0.554163:0.316376:0.000000 x:@0.582252:0.330647:0.589707:0.330647:0.589707:0.314241:0.582252:0.314241:0.000000 5:@0.593591:0.330092:0.608925:0.330092:0.608925:0.316376:0.593591:0.316376:0.000000 x:@0.617576:0.330647:0.625031:0.330647:0.625031:0.314241:0.617576:0.314241:0.000000 2:@0.628915:0.330092:0.644248:0.330092:0.644248:0.316376:0.628915:0.316376:0.000000 2:@0.661817:0.324585:0.667054:0.324585:0.667054:0.315004:0.661817:0.315004:0.000000 2:@0.670964:0.330095:0.686297:0.330095:0.686297:0.316379:0.670964:0.316379:0.000000 Solución:@0.293670:0.358011:0.359804:0.358011:0.359804:0.341342:0.293670:0.341342:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.293670:0.385373:0.301125:0.385373:0.301125:0.368967:0.293670:0.368967:0.000000 2:@0.301048:0.379312:0.306285:0.379312:0.306285:0.369731:0.301048:0.369731:0.000000 6 6 2 1 17 :@0.306239:0.385376:0.556494:0.385376:0.556494:0.368942:0.306239:0.368942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 2 2:@0.310197:0.384821:0.384157:0.384821:0.384157:0.371105:0.310197:0.371105:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.329395:0.385376:0.336850:0.385376:0.336850:0.368970:0.329395:0.368970:0.000000 x:@0.396913:0.385376:0.404368:0.385376:0.404368:0.368970:0.396913:0.368970:0.000000 5:@0.408252:0.384821:0.423585:0.384821:0.423585:0.371105:0.408252:0.371105:0.000000 x:@0.427451:0.385376:0.434906:0.385376:0.434906:0.368970:0.427451:0.368970:0.000000 2:@0.434827:0.379312:0.440064:0.379312:0.440064:0.369731:0.434827:0.369731:0.000000 2:@0.443975:0.384821:0.459309:0.384821:0.459309:0.371105:0.443975:0.371105:0.000000 x:@0.472065:0.385376:0.479520:0.385376:0.479520:0.368970:0.472065:0.368970:0.000000 1 2:@0.483404:0.384821:0.530784:0.384821:0.530784:0.371105:0.483404:0.371105:0.000000:0.000000:0.000000 Desarrollamos los productos notables.:@0.594873:0.385376:0.871645:0.385376:0.871645:0.368942:0.594873:0.368942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.293660:0.412739:0.301115:0.412739:0.301115:0.396333:0.293660:0.396333:0.000000 2:@0.301048:0.406675:0.306285:0.406675:0.306285:0.397094:0.301048:0.397094:0.000000 6 2 1 17 6 :@0.306239:0.412739:0.556469:0.412739:0.556469:0.396305:0.306239:0.396305:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 2:@0.310197:0.412184:0.356067:0.412184:0.356067:0.398469:0.310197:0.398469:0.000000:0.000000:0.000000 x:@0.329395:0.412739:0.336850:0.412739:0.336850:0.396333:0.329395:0.396333:0.000000 x:@0.364884:0.412739:0.372339:0.412739:0.372339:0.396333:0.364884:0.396333:0.000000 2:@0.376223:0.412184:0.391557:0.412184:0.391557:0.398469:0.376223:0.398469:0.000000 x:@0.395422:0.412739:0.402877:0.412739:0.402877:0.396333:0.395422:0.396333:0.000000 2:@0.402783:0.406675:0.408020:0.406675:0.408020:0.397094:0.402783:0.397094:0.000000 1:@0.411930:0.412184:0.427263:0.412184:0.427263:0.398469:0.411930:0.398469:0.000000 x:@0.440020:0.412739:0.447474:0.412739:0.447474:0.396333:0.440020:0.396333:0.000000 5 2:@0.451358:0.412184:0.498739:0.412184:0.498739:0.398469:0.451358:0.398469:0.000000:0.000000:0.000000 1:@0.524343:0.412184:0.539676:0.412184:0.539676:0.398469:0.524343:0.398469:0.000000 Trasponemos los términos que contienen :@0.594866:0.412739:0.930943:0.412739:0.930943:0.396305:0.594866:0.396305:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a la incógnita.:@0.594895:0.429381:0.695065:0.429381:0.695065:0.412947:0.594895:0.412947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.293660:0.456189:0.308993:0.456189:0.308993:0.442474:0.293660:0.442474:0.000000 5 10:@0.308901:0.456744:0.381468:0.456744:0.381468:0.440310:0.308901:0.440310:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.317810:0.456744:0.325265:0.456744:0.325265:0.440338:0.317810:0.440338:0.000000 5 2:@0.329149:0.456189:0.363681:0.456189:0.363681:0.442474:0.329149:0.442474:0.000000:0.000000:0.000000 Reducimos términos semejantes.:@0.594900:0.456744:0.834514:0.456744:0.834514:0.440310:0.594900:0.440310:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 5 2:@0.293660:0.487088:0.354772:0.487088:0.354772:0.473372:0.293660:0.473372:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.308901:0.487642:0.316356:0.487642:0.316356:0.471236:0.308901:0.471236:0.000000 :@0.316283:0.487642:0.339513:0.487642:0.339513:0.471208:0.316283:0.471208:0.000000:0.000000:0.000000 10:@0.357045:0.482427:0.374918:0.482427:0.374918:0.465993:0.357045:0.465993:0.000000:0.000000 5:@0.361499:0.496406:0.370482:0.496406:0.370482:0.479972:0.361499:0.479972:0.000000 Pasamos 5 a dividir.:@0.594878:0.487642:0.734608:0.487642:0.734608:0.471208:0.594878:0.471208:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.293660:0.515006:0.301115:0.515006:0.301115:0.498599:0.293660:0.498599:0.000000 2 :@0.301041:0.515006:0.337138:0.515006:0.337138:0.498572:0.301041:0.498572:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.304999:0.514451:0.320332:0.514451:0.320332:0.500735:0.304999:0.500735:0.000000 Multiplicamos los dos miembros por 1.:@0.594876:0.515006:0.890964:0.515006:0.890964:0.498572:0.594876:0.498572:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.863611:0.514451:0.878944:0.514451:0.878944:0.500735:0.863611:0.500735:0.000000 Cuando la ecuación tiene términos fraccionarios, se busca el mcm. de los :@0.301224:0.544857:0.923527:0.544857:0.923527:0.528424:0.301224:0.528424:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 denominadores; lo dividimos entre cada denominador y multiplicamos por el :@0.301224:0.561499:0.923194:0.561499:0.923194:0.545065:0.301224:0.545065:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 numerador. Al pasar el mcm. del primer miembro al segundo miembro, este se :@0.301224:0.578141:0.923258:0.578141:0.923258:0.561707:0.301224:0.561707:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 simplifica. De este modo, la ecuación deja de tener denominadores y se resuelve :@0.301224:0.594783:0.923700:0.594783:0.923700:0.578349:0.301224:0.578349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 siguiendo las reglas anteriores.:@0.301224:0.611425:0.522315:0.611425:0.522315:0.594991:0.301224:0.594991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ejemplo 3:@0.293658:0.645832:0.369441:0.645832:0.369441:0.629162:0.293658:0.629162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Resuelve la ecuación :@0.293658:0.676730:0.448412:0.676730:0.448412:0.660296:0.293658:0.660296:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.455026:0.671509:0.464009:0.671509:0.464009:0.655076:0.455026:0.655076:0.000000 2:@0.455026:0.685488:0.464009:0.685488:0.464009:0.669055:0.455026:0.669055:0.000000 x:@0.470746:0.676724:0.478201:0.676724:0.478201:0.660318:0.470746:0.660318:0.000000 :@0.478128:0.676724:0.501358:0.676724:0.501358:0.660290:0.478128:0.660290:0.000000:0.000000:0.000000 2:@0.482085:0.676169:0.497418:0.676169:0.497418:0.662453:0.482085:0.662453:0.000000 4:@0.508096:0.671509:0.517079:0.671509:0.517079:0.655076:0.508096:0.655076:0.000000 3:@0.508096:0.685488:0.517079:0.685488:0.517079:0.669055:0.508096:0.669055:0.000000 :@0.523816:0.676724:0.547046:0.676724:0.547046:0.660290:0.523816:0.660290:0.000000:0.000000:0.000000 5:@0.527774:0.676169:0.543107:0.676169:0.543107:0.662453:0.527774:0.662453:0.000000 2:@0.553776:0.671509:0.562759:0.671509:0.562759:0.655076:0.553776:0.655076:0.000000 5:@0.553776:0.685488:0.562759:0.685488:0.562759:0.669055:0.553776:0.669055:0.000000 4 .:@0.569496:0.676724:0.608188:0.676724:0.608188:0.660290:0.569496:0.660290:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.573454:0.676169:0.588787:0.676169:0.588787:0.662453:0.573454:0.662453:0.000000 x:@0.597604:0.676724:0.605059:0.676724:0.605059:0.660318:0.597604:0.660318:0.000000 Solución:@0.293663:0.704086:0.359797:0.704086:0.359797:0.687416:0.293663:0.687416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.300478:0.729771:0.309460:0.729771:0.309460:0.713337:0.300478:0.713337:0.000000 2:@0.300478:0.743750:0.309460:0.743750:0.309460:0.727316:0.300478:0.727316:0.000000 x:@0.316197:0.734985:0.323652:0.734985:0.323652:0.718579:0.316197:0.718579:0.000000 :@0.323579:0.734985:0.346809:0.734985:0.346809:0.718552:0.323579:0.718552:0.000000:0.000000:0.000000 2:@0.327536:0.734431:0.342869:0.734431:0.342869:0.720715:0.327536:0.720715:0.000000 4:@0.353549:0.729771:0.362532:0.729771:0.362532:0.713337:0.353549:0.713337:0.000000 3:@0.353549:0.743750:0.362532:0.743750:0.362532:0.727316:0.353549:0.727316:0.000000 :@0.369269:0.734985:0.392499:0.734985:0.392499:0.718552:0.369269:0.718552:0.000000:0.000000:0.000000 5:@0.373226:0.734431:0.388560:0.734431:0.388560:0.720715:0.373226:0.720715:0.000000 2:@0.399229:0.729771:0.408212:0.729771:0.408212:0.713337:0.399229:0.713337:0.000000 5:@0.399229:0.743750:0.408212:0.743750:0.408212:0.727316:0.399229:0.727316:0.000000 4:@0.414949:0.734985:0.447088:0.734985:0.447088:0.718552:0.414949:0.718552:0.000000:0.000000:0.000000:0.000000 2:@0.418906:0.734431:0.434240:0.734431:0.434240:0.720715:0.418906:0.720715:0.000000 x :@0.446994:0.734987:0.477698:0.734987:0.477698:0.718581:0.446994:0.718581:0.000000:0.000000:0.000000 Determinamos el mcm de 2, 3, 5 y 1; en este caso es 30.:@0.534628:0.734987:0.926767:0.734987:0.926767:0.718553:0.534628:0.718553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 15 40:@0.299447:0.763529:0.365676:0.763529:0.365676:0.747095:0.299447:0.747095:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.317247:0.763529:0.324701:0.763529:0.324701:0.747123:0.317247:0.747123:0.000000 2:@0.328585:0.762974:0.343919:0.762974:0.343919:0.749258:0.328585:0.749258:0.000000 30:@0.323615:0.777508:0.341507:0.777508:0.341507:0.761074:0.323615:0.761074:0.000000:0.000000 5:@0.375323:0.768191:0.390656:0.768191:0.390656:0.754475:0.375323:0.754475:0.000000 :@0.390564:0.768746:0.394595:0.768746:0.394595:0.752312:0.390564:0.752312:0.000000 12 120:@0.397608:0.763529:0.465365:0.763529:0.465365:0.747095:0.397608:0.747095:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.419365:0.762974:0.434698:0.762974:0.434698:0.749258:0.419365:0.749258:0.000000 x:@0.465254:0.763529:0.472709:0.763529:0.472709:0.747123:0.465254:0.747123:0.000000 30:@0.426212:0.777508:0.444104:0.777508:0.444104:0.761074:0.426212:0.761074:0.000000:0.000000 Dividimos el mcm para cada denominador :@0.534631:0.768746:0.848764:0.768746:0.848764:0.752312:0.534631:0.752312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y multiplicamos por los numeradores.:@0.534629:0.785387:0.807977:0.785387:0.807977:0.768954:0.534629:0.768954:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 15 40 :@0.293660:0.819145:0.383009:0.819145:0.383009:0.802711:0.293660:0.802711:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.311460:0.819145:0.318915:0.819145:0.318915:0.802739:0.311460:0.802739:0.000000 2:@0.322799:0.818590:0.338132:0.818590:0.338132:0.804875:0.322799:0.804875:0.000000 5:@0.363737:0.818590:0.379070:0.818590:0.379070:0.804875:0.363737:0.804875:0.000000 12 120:@0.386034:0.813929:0.453792:0.813929:0.453792:0.797496:0.386034:0.797496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.407792:0.813375:0.423125:0.813375:0.423125:0.799659:0.407792:0.799659:0.000000 x:@0.453681:0.813929:0.461136:0.813929:0.461136:0.797523:0.453681:0.797523:0.000000 30:@0.414639:0.827909:0.432531:0.827909:0.432531:0.811475:0.414639:0.811475:0.000000:0.000000 30 :@0.464155:0.819144:0.509154:0.819145:0.509154:0.802711:0.464155:0.802710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.468112:0.818589:0.483446:0.818589:0.483446:0.804873:0.468112:0.804873:0.000000 Pasamos el mcm del primer miembro al segundo.:@0.534629:0.819145:0.895106:0.819145:0.895106:0.802711:0.534629:0.802711:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 15 40 12 120:@0.293660:0.849368:0.450674:0.849368:0.450674:0.832934:0.293660:0.832934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.311460:0.849368:0.318915:0.849368:0.318915:0.832962:0.311460:0.832962:0.000000 2:@0.322799:0.848813:0.338132:0.848813:0.338132:0.835097:0.322799:0.835097:0.000000 5:@0.363737:0.848813:0.379070:0.848813:0.379070:0.835097:0.363737:0.835097:0.000000 2:@0.404674:0.848813:0.420008:0.848813:0.420008:0.835097:0.404674:0.835097:0.000000 x :@0.450595:0.849368:0.477691:0.849368:0.477691:0.832962:0.450595:0.832962:0.000000:0.000000:0.000000 Simplificamos:@0.534628:0.849368:0.636089:0.849368:0.636089:0.832934:0.534628:0.832934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.635923:0.849368:0.639255:0.849368:0.639255:0.832962:0.635923:0.832962:0.000000 15 120 12 40 :@0.293658:0.879586:0.462028:0.879589:0.462028:0.863155:0.293658:0.863153:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.311458:0.879586:0.318913:0.879586:0.318913:0.863180:0.311458:0.863180:0.000000 1:@0.322797:0.879032:0.338130:0.879032:0.338130:0.865316:0.322797:0.865316:0.000000 x:@0.368686:0.879586:0.376141:0.879586:0.376141:0.863180:0.368686:0.863180:0.000000 5:@0.380025:0.879032:0.395359:0.879032:0.395359:0.865316:0.380025:0.865316:0.000000 1:@0.420963:0.879032:0.436296:0.879032:0.436296:0.865316:0.420963:0.865316:0.000000 Trasponemos los términos que contienen la incógnita :@0.534633:0.879589:0.930943:0.879589:0.930943:0.863155:0.534633:0.863155:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 al primer miembro y los números al segundo.:@0.534629:0.896231:0.863681:0.896231:0.863681:0.879797:0.534629:0.879797:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.293660:0.930883:0.301115:0.930883:0.301115:0.914477:0.293660:0.914477:0.000000 :@0.301041:0.930883:0.324271:0.930883:0.324271:0.914449:0.301041:0.914449:0.000000:0.000000:0.000000 5:@0.304999:0.930328:0.320332:0.930328:0.320332:0.916612:0.304999:0.916612:0.000000 52:@0.332499:0.924773:0.350391:0.924773:0.350391:0.908339:0.332499:0.908339:0.000000:0.000000 135:@0.328045:0.938752:0.354846:0.938752:0.354846:0.922319:0.328045:0.922319:0.000000:0.000000:0.000000 Competencia :@0.078581:0.144831:0.187141:0.144831:0.187141:0.127884:0.078581:0.127884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.078581:0.161472:0.176057:0.161472:0.176057:0.144526:0.078581:0.144526:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Para verificar si la solución :@0.078581:0.182996:0.252325:0.182996:0.252325:0.168056:0.078581:0.168056:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de la ecuacion es correcta :@0.078581:0.198125:0.253532:0.198125:0.253532:0.183185:0.078581:0.183185:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 se reemplaza el valor :@0.078581:0.213254:0.219868:0.213254:0.219868:0.198314:0.078581:0.198314:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 obtenido de la incógnita :@0.078581:0.228383:0.244885:0.228383:0.244885:0.213443:0.078581:0.213443:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en la ecuación y se verifica :@0.078581:0.243512:0.256649:0.243512:0.256649:0.228572:0.078581:0.228572:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la veracidad de la igualdad.:@0.078581:0.258641:0.256952:0.258641:0.256952:0.243701:0.078581:0.243701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 6 13 23:@0.078581:0.277337:0.167923:0.277337:0.167923:0.262398:0.078581:0.262398:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.086680:0.277337:0.093457:0.277337:0.093457:0.262423:0.086680:0.262423:0.000000 2:@0.096988:0.276833:0.110927:0.276833:0.110927:0.264364:0.096988:0.264364:0.000000 5:@0.134204:0.276833:0.148144:0.276833:0.148144:0.264364:0.134204:0.264364:0.000000 6 23 13:@0.078581:0.296034:0.167923:0.296034:0.167923:0.281094:0.078581:0.281094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.086680:0.296034:0.093457:0.296034:0.093457:0.281120:0.086680:0.281120:0.000000 5:@0.096988:0.295530:0.110927:0.295530:0.110927:0.283061:0.096988:0.283061:0.000000 1:@0.134204:0.295530:0.148144:0.295530:0.148144:0.283061:0.134204:0.283061:0.000000 6 36:@0.078581:0.314731:0.130707:0.314731:0.130707:0.299791:0.078581:0.299791:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.086680:0.314731:0.093457:0.314731:0.093457:0.299817:0.086680:0.299817:0.000000 5:@0.096988:0.314227:0.110927:0.314227:0.110927:0.301758:0.096988:0.301758:0.000000 x:@0.078581:0.338231:0.085358:0.338231:0.085358:0.323317:0.078581:0.323317:0.000000 :@0.085291:0.338231:0.106409:0.338231:0.106409:0.323292:0.085291:0.323292:0.000000:0.000000:0.000000 5:@0.088889:0.337727:0.102828:0.337727:0.102828:0.325258:0.088889:0.325258:0.000000 36:@0.108708:0.333347:0.126581:0.333347:0.126581:0.316913:0.108708:0.316913:0.000000:0.000000 6:@0.113162:0.347326:0.122145:0.347326:0.122145:0.330893:0.113162:0.330893:0.000000 6 36:@0.078581:0.360524:0.130707:0.360524:0.130707:0.345584:0.078581:0.345584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.086680:0.360524:0.093457:0.360524:0.093457:0.345609:0.086680:0.345609:0.000000 5:@0.096988:0.360020:0.110927:0.360020:0.110927:0.347551:0.096988:0.347551:0.000000 Comprobación:@0.078581:0.379221:0.181990:0.379221:0.181990:0.364067:0.078581:0.364067:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 6(6) 13 23:@0.078581:0.394356:0.182337:0.394356:0.182337:0.379416:0.078581:0.379416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.111402:0.393852:0.125341:0.393852:0.125341:0.381383:0.111402:0.381383:0.000000 5:@0.148618:0.393852:0.162557:0.393852:0.162557:0.381383:0.148618:0.381383:0.000000 36 13 23:@0.078581:0.413059:0.182337:0.413059:0.182337:0.398119:0.078581:0.398119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.111402:0.412555:0.125341:0.412555:0.125341:0.400086:0.111402:0.400086:0.000000 5:@0.148618:0.412555:0.162557:0.412555:0.162557:0.400086:0.148618:0.400086:0.000000 23:@0.128849:0.431761:0.145048:0.431761:0.145048:0.416821:0.128849:0.416821:0.000000:0.000000 5:@0.148626:0.431257:0.162565:0.431257:0.162565:0.418788:0.148626:0.418788:0.000000 23:@0.162482:0.431761:0.182345:0.431761:0.182345:0.416821:0.162482:0.416821:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000