document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85471>Question 85471</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0073048313/algebrahomeworkh>algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am having to multiply the fractions, please show me how to do this.\r<BR>\n" );
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document.write( "2x^2-x-3    3x^2-11x-20<BR>\n" );
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document.write( "3x^2+7x+4    4x^2-9\r<BR>\n" );
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document.write( "I really need the help, thanks<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61724 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=61724\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282%2Ax%5E2+-x+-+3%29%2F%283%2Ax%5E2+%2B+7%2Ax+%2B+4%29%29%2A%28%283%2Ax%5E2+-+11%2Ax+-+20%29%2F%284%2Ax%5E2+-+9%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28x%2B1%29%282%2Ax-3%29%29%2F%283%2Ax%5E2+%2B+7%2Ax+%2B+4%29%29%2A%28%283%2Ax%5E2+-+11%2Ax+-+20%29%2F%284%2Ax%5E2+-+9%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the first numerator (note: if you need help with factoring, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/quadratic-factoring.solver>solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28x%2B1%29%282%2Ax-3%29%29%2F%28%28x%2B1%29%283%2Ax%2B4%29%29%29%2A%28%283%2Ax%5E2+-+11%2Ax+-+20%29%2F%284%2Ax%5E2+-+9%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the first denominator \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28x%2B1%29%282%2Ax-3%29%29%2F%28%28x%2B1%29%283%2Ax%2B4%29%29%29%2A%28%28%283%2Ax%2B4%29%28x-5%29%29%2F%284%2Ax%5E2+-+9%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the second numerator \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28x%2B1%29%282%2Ax-3%29%29%2F%28%28x%2B1%29%283%2Ax%2B4%29%29%29%2A%28%28%283%2Ax%2B4%29%28x-5%29%29%2F%28%282%2Ax%2B3%29%282%2Ax-3%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the second denominator \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28highlight%28%28x%2B1%29%29highlight%28%282%2Ax-3%29%29%29%2F%28highlight%28%28x%2B1%29%29highlight%28%283%2Ax%2B4%29%29%29%29%2A%28%28highlight%28%283%2Ax%2B4%29%29%28x-5%29%29%2F%28%282%2Ax%2B3%29highlight%28%282%2Ax-3%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Notice we have these common terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28cross%28%28x%2B1%29%29cross%28%282%2Ax-3%29%29%29%2F%28cross%28%28x%2B1%29%29cross%28%283%2Ax%2B4%29%29%29%29%2A%28%28cross%28%283%2Ax%2B4%29%29%28x-5%29%29%2F%28%282%2Ax%2B3%29cross%28%282%2Ax-3%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > They divide and cancel out\r<BR>\n" );
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document.write( "Leaving you with this:\r<BR>\n" );
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document.write( "So the expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282%2Ax%5E2+-x+-+3%29%2F%283%2Ax%5E2+%2B+7%2Ax+%2B+4%29%29%2A%28%283%2Ax%5E2+-+11%2Ax+-+20%29%2F%284%2Ax%5E2+-+9%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplifies to\r<BR>\n" );
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document.write( "As always, we can verify our answer. We can graph the original expression\r<BR>\n" );
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document.write( "as a function of y like this\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+%28%282%2Ax%5E2+-x+-+3%29%2F%283%2Ax%5E2+%2B+7%2Ax+%2B+4%29%29%2A%28%283%2Ax%5E2+-+11%2Ax+-+20%29%2F%284%2Ax%5E2+-+9%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > graph of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%282%2Ax%5E2+-x+-+3%29%2F%283%2Ax%5E2+%2B+7%2Ax+%2B+4%29%29%2A%28%283%2Ax%5E2+-+11%2Ax+-+20%29%2F%284%2Ax%5E2+-+9%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and graph the simplified result\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C%28%28x-5%29%2F%282%2Ax%2B3%29%29%29 ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C%28%28x-5%29%2F%282%2Ax%2B3%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-5%29%2F%282%2Ax%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28%28x-5%29%2F%282%2Ax%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since they produce the same graphs, this means they are equivalent. Since they are equivalent, this means that our answer has been verified.<BR>\n" );
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