136

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=24 BGCOLOR="#003333" TEXT="#F7F7FF"> <div> <FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" ><B>M</B></FONT><FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" ><B>atemáticas de la U</B></FONT><B> (MatU)  | </B><A HREF="http://www.jcbmat.com/" TARGET="_top" TITLE="http://www.jcbmat.com/"><U><B>Home</B></U></A><B> | </B><A HREF="index.htm" TARGET="_top" TITLE="Álgebra de Baldor"><U><B>Algebra de Baldor</B></U></A><B> |  </B><A HREF="id1076.htm" TARGET="_top" TITLE="Índice temático"><U><B>Índice temático</B></U></A><B>  |  </B><A HREF="id1073.htm" TARGET="_top" TITLE="Lista"><U><B>Lista de Ejercicios</B></U></A><B> |</B></div> </td> </tr><tr> <td valign="top" rowspan="2" width=165 BGCOLOR="#FFFFFF" TEXT="#080000"> <bR> <div> <B> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:160px;height:600px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="3073775660"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </B></div> </td> <td valign="top" height=432 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B>136</B></div> <div> <B>Operaciones con fracciones</B></div> <div> <B>Multiplicación y división combinadas</B></div> <bR> <div>  <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:970px;height:250px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="8553279920"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> <bR> <div> <B>P r o c e d i m i e n t o :</B></div> <div> <FONT SIZE="4" COLOR="#FF6600" FACE="Bell MT" ><B>1.</B></FONT><B> </B> Se invierten las fracciones precedidas del signo de la división y se cambia el signo operativo por el de la multiplicación,  por la x </div> <div> <FONT SIZE="4" COLOR="#FF6600" FACE="Bell MT" ><B>2.</B></FONT><B> </B> Las fracciones se multiplican siguiendo los pasos siguientes:</div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><B>    </B></FONT><B>a</B>)<FONT SIZE="4" COLOR="#000000" FACE="Bell MT" > Se factorizan los polinomios</FONT></div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >    </FONT><B>b</B>)<FONT SIZE="4" COLOR="#000000" FACE="Bell MT" > Se simplifica, suprimiendo los factores iguales presentes tanto en un numerador como en un denominador de alguna de las fracciones</FONT></div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >    </FONT><B>c</B>)<FONT SIZE="4" COLOR="#000000" FACE="Bell MT" > Se multiplican entre sí las expresiones que quedan en los numeradores; lo propio se hace con las expresiones que quedan en los denominadores; luego, para el resultado, se ubica en el numerador el producto de los numeradores y en el denominador el producto de los denominadores </FONT></div> <div> <B>Consejo</B>:<FONT SIZE="4" COLOR="#000000" FACE="Bell MT" > Para realizar los ejercicios siguientes es indispensable dominar por completo la factorización, por lo cual recomiendo que se estudie primero concienzudamente los 10 casos de factorización (Ejercicios 89 a 110).</FONT></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>Enunciados de los ejercicios</B></div> <bR> <div> <FONT SIZE="5" COLOR="#006600" FACE="Bell MT" ><B>S</B></FONT>olución en imagen <IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> y o video <IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> de los catorce problemas del Ejercicio 136:</div> <div> <B>S</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >ultiplicar:</FONT></div> <div> <IMG SRC="80f089330.gif" border=0 width="137" height="51" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#1" TITLE="136"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/5MjSVG2iN6U" TARGET="_top" TITLE="https://youtu.be/5MjSVG2iN6U"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="80f19d340.gif" border=0 width="157" height="52" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#2" TITLE="136"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/5MjSVG2iN6U" TARGET="_top" TITLE="https://youtu.be/5MjSVG2iN6U"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="80f2e0310.gif" border=0 width="224" height="49" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#3" TITLE="136"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/Sl6IYSxQ7N4" TARGET="_top" TITLE="https://youtu.be/Sl6IYSxQ7N4"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> </div> <div> <IMG SRC="80f324350.gif" border=0 width="292" height="53" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#4" TITLE="136"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/Sl6IYSxQ7N4" TARGET="_top" TITLE="https://youtu.be/Sl6IYSxQ7N4"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>        <IMG SRC="80f444310.gif" border=0 width="324" height="49" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#5" TITLE="136"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/trFsaNq-BJY" TARGET="_top" TITLE="https://youtu.be/trFsaNq-BJY"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>  </div> <div> <IMG SRC="80f534310.gif" border=0 width="308" height="49" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#6" TITLE="136"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/trFsaNq-BJY" TARGET="_top" TITLE="https://youtu.be/trFsaNq-BJY"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="80fd4c310.gif" border=0 width="332" height="49" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://youtu.be/XW11wRB9_1M" TARGET="_top" TITLE="https://youtu.be/XW11wRB9_1M"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="80fee5390.gif" border=0 width="229" height="57" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://youtu.be/XW11wRB9_1M" TARGET="_top" TITLE="https://youtu.be/XW11wRB9_1M"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="810f45310.gif" border=0 width="325" height="49" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://youtu.be/pJWmOgUkTU8" TARGET="_top" TITLE="https://youtu.be/pJWmOgUkTU8"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="8110433f0.gif" border=0 width="323" height="63" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://youtu.be/pJWmOgUkTU8" TARGET="_top" TITLE="https://youtu.be/pJWmOgUkTU8"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="81453d390.gif" border=0 width="317" height="57" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://youtu.be/7eaZRiF4g9I" TARGET="_top" TITLE="https://youtu.be/7eaZRiF4g9I"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="80f6d0310.gif" border=0 width="464" height="49" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://youtu.be/306F24Foc7U" TARGET="_top" TITLE="https://youtu.be/306F24Foc7U"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="8146a0410.gif" border=0 width="416" height="65" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://youtu.be/7eaZRiF4g9I" TARGET="_top" TITLE="https://youtu.be/7eaZRiF4g9I"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="80f745490.gif" border=0 width="325" height="73" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="https://youtu.be/hr6dYG2R2aI" TARGET="_top" TITLE="https://youtu.be/hr6dYG2R2aI"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>Lista de reproducción en YouTube del Ejercicio 136</B></div> <bR> <div> <B> <iframe width="560" height="315" src="https://www.youtube.com/embed/videoseries?list=PLq_SQwoOZHo0531w3_nVO5qcyupOPaCTK" frameborder="0" allow="autoplay; encrypted-media" allowfullscreen></iframe>  </B></div> <div> <B>S </B><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >i m p l i f i c a r :</FONT></div> <div>  <A NAME="1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>1</div> <div> <IMG SRC="5f4655170.gif" border=0 width="597" height="279" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>2</div> <div> <IMG SRC="5f4773140.gif" border=0 width="627" height="276" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="3"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>3</div> <div> <IMG SRC="5f488b450.gif" border=0 width="651" height="325" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="4"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>4</div> <div> <IMG SRC="5e5619500.gif" border=0 width="793" height="336" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="5"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>5</div> <div> <IMG SRC="5f4948450.gif" border=0 width="840" height="325" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="6"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>6</div> <div> <IMG SRC="5e5739430.gif" border=0 width="825" height="323" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <bR> <DIV ALIGN="LEFT"></DIV> <div> <A HREF="http://twitter.com/Calculo21" TARGET="_top" TITLE="http://twitter.com/Calculo21"><U><IMG SRC="2fc828280.jpg" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="http://www.facebook.com/juan.beltran.58511" TARGET="_top" TITLE="http://www.facebook.com/juan.beltran.585"><U><IMG SRC="76fa28280.gif" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://www.youtube.com/user/MatematicaAplicadas" TARGET="_top" TITLE="https://www.youtube.com/user/MatematicaA"><U><IMG SRC="2fca28280.jpg" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <bR> <div> Por: <FONT SIZE="4" COLOR="#FF9900" FACE="Times New Roman" >Juan Carlos 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