document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=825738>Question 825738</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Multiply\r<BR>\n" );
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document.write( "(x+4)/(x^2+2x+1)*(x+1)/(x^2-16)\r<BR>\n" );
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document.write( "(x^2-9)/(x^2+x-12)*(x^2-16)/(3)\r<BR>\n" );
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document.write( "Please help me with this! Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497567 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=497567\">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%28x%2B4%29%2F%28x%5E2%2B2x%2B1%29%29%2A%28%28x%2B1%29%2F%28x%5E2-16%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B4%29%2F%28x%5E2%2B2x%2B1%29%29%2A%28%28x%2B1%29%2F%28x%5E2-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Way back in the \"good ole days\", when fractions had numbers for numerators and denominators, you should have learned that when multiplying fractions...<ul><li>It is OK to cancel before multiplying. In fact this the only time when it is OK to cancel a factor in one fraction's numerator with a factor in another fraction's denominator. (This is called \"cross-canceling\" and is allowed <u>only</u> when multiplying fractions.)</li><li>Not only is it OK, it is a good idea. Canceling before multiplying makes the rest of the problem easier!</li></ul>All of this is still true for these more complex fractions with variables in them. In fact, the advantage in canceling first is much greater with these fractions than it was with the simpler fractions!! So don't even think about multiplying first!<br><BR>\n" );
document.write( "To cancel first we must know what the factors of each numerator and denominator are. So we start by factoring:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%28x%2B4%29%29%2F%28%28x%2B1%29%28x%2B1%29%29%29%2A%28%281%28x%2B1%29%29%2F%28%28x%2B4%29%28x-4%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As we can see, there are many factor we can cancel:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2Across%28%28x%2B4%29%29%29%2F%28cross%28%28x%2B1%29%29%28x%2B1%29%29%29%2A%28%281%2Across%28%28x%2B1%29%29%29%2F%28cross%28%28x%2B4%29%29%28x-4%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "leaving:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28x%2B1%29%29%2A%281%2F%28x-4%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%28x%2B1%29%29%2A%281%2F%28x-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The advantage of canceling first should be obvious. These two fractions will be much easier to multiply than the original fractions! Multiplying we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x%5E2-3x-4%29 ALIGN=MIDDLE  ALT=\"1%2F%28x%5E2-3x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "I'll leave the second problem for you to do. Be sure to factor and cancel first!<br><BR>\n" );
document.write( "P.S. I think the second problem should be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2-9%29%2F%28x%5E2%2Bx-12%29%29%2A%28%28x%5E2-16%29%2F%28x-3%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%5E2-9%29%2F%28x%5E2%2Bx-12%29%29%2A%28%28x%5E2-16%29%2F%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2-9%29%2F%28x%5E2%2Bx-12%29%29%2A%28%28x%5E2-16%29%2F%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%5E2-9%29%2F%28x%5E2%2Bx-12%29%29%2A%28%28x%5E2-16%29%2F%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and not what you posted:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2-9%29%2F%28x%5E2%2Bx-12%29%29%2A%28%28x%5E2-16%29%2F%283%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%5E2-9%29%2F%28x%5E2%2Bx-12%29%29%2A%28%28x%5E2-16%29%2F%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "P.P.S. This problem is <i>not</i> a rational function. It is a rational expression which should be posted in the \"polynomials, rational expressions...\" category. </SPAN>\n" );
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