document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=698436>Question 698436</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (4u^2 - 1)/(u^3 - 16u) * (u^2 + 4u)/(2u - 1)\r<BR>\n" );
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document.write( "The answer the book has is (2u + 1) / (u -4)\r<BR>\n" );
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document.write( "It am a parent and I can't figure this out to explain to my homeschooled child. The chapter is multiplying and dividing rational expressions. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #430648 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=430648\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4u^2 - 1\r<BR>\n" );
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document.write( "factors to\r<BR>\n" );
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document.write( "(2u + 1)(2u - 1)\r<BR>\n" );
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document.write( "using the difference of squares rule\r<BR>\n" );
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document.write( "The second term \"(2u - 1)\" cancels with the last term \"(2u - 1)\" on the very right.\r<BR>\n" );
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document.write( "u^3 - 16u\r<BR>\n" );
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document.write( "factors to\r<BR>\n" );
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document.write( "u(u^2 - 16)\r<BR>\n" );
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document.write( "which further factors to\r<BR>\n" );
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document.write( "u(u-4)(u+4)\r<BR>\n" );
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document.write( "using the difference of squares rule\r<BR>\n" );
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document.write( "u^2 + 4u\r<BR>\n" );
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document.write( "factors to\r<BR>\n" );
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document.write( "u(u + 4)\r<BR>\n" );
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document.write( "Notice the last two final factorizations have a 'u' and a 'u+4' in common. They cancel\r<BR>\n" );
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document.write( "So after all of the factorizations and cancellations, we go from \r<BR>\n" );
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document.write( "(4u^2 - 1)/(u^3 - 16u) * (u^2 + 4u)/(2u - 1)\r<BR>\n" );
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document.write( "to\r<BR>\n" );
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document.write( "((2u - 1)(2u + 1))/(u(u-4)(u+4)) * (u(u+4))/(2u - 1)\r<BR>\n" );
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document.write( "which simplifies to\r<BR>\n" );
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document.write( "(2u + 1) / (u-4) </SPAN>\n" );
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