document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=854077>Question 854077</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify the rational expression.<BR>\n" );
document.write( "(9x^3-41x^2-20x) / (yx^2-2yx-15y) \r<BR>\n" );
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document.write( "Would you factor it like this? <BR>\n" );
document.write( "9x^3-45x^2+4x^2-20x / yx^2+3yx-5yx-15y\r<BR>\n" );
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document.write( "Thank you for your help!<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 #514849 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=514849\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> problem is:\r<BR>\n" );
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document.write( "Simplify the rational expression.<BR>\n" );
document.write( "(9x^3-41x^2-20x) / (yx^2-2yx-15y) \r<BR>\n" );
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document.write( "factor out an x in the numerator to get x * (9x^2 - 41x - 20)\r<BR>\n" );
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document.write( "factor out a y in the denominator to get y * (x^2 - 2x - 15)\r<BR>\n" );
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document.write( "your expression becomes:\r<BR>\n" );
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document.write( "x * (9x^2 - 41x - 20) / (y * (x^2 - 2x - 15)\r<BR>\n" );
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document.write( "factor 9x^2 - 41x - 20 in the numerator to get x * (9x + 4) * (x - 5)\r<BR>\n" );
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document.write( "factor x^2 - 2x - 15 in the denominator to get y * (x - 5) * (x + 3)\r<BR>\n" );
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document.write( "your expression becomes:\r<BR>\n" );
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document.write( "[x * (9x + 4) * (x = 5)] / [y * (x - 5) * (x + 3)]\r<BR>\n" );
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document.write( "the (x-5) in the numerator cancels out the (x-5) in the denominator and you are left with:\r<BR>\n" );
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document.write( "(x * (9x + 4)] / [y * (x + 3)]\r<BR>\n" );
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document.write( "if you simplify this, you will get:\r<BR>\n" );
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document.write( "(9x^2 + 4x) / (yx + 3y)\r<BR>\n" );
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document.write( "that should be it.\r<BR>\n" );
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document.write( "there are many different ways to factor a quadratic.\r<BR>\n" );
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document.write( "you last resort, if you can't do it any other way, is the quadratic formula.\r<BR>\n" );
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document.write( "that formula is x = [-b +/- sqrt(b^2 - 4ac)] / 2a\r<BR>\n" );
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document.write( "once you find the roots, you then  need to set the root equal to 0 in order to find the factor.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "the factor of 9x + 4 creates the root of x = -4/9.\r<BR>\n" );
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document.write( "the quadratic formula will give you that root, but it will not give you the factor that created that root.\r<BR>\n" );
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document.write( "to find the factor you would do the following:\r<BR>\n" );
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document.write( "start with x = -4/9<BR>\n" );
document.write( "multiply both sides of this equation by 9 to get:<BR>\n" );
document.write( "9x = -4<BR>\n" );
document.write( "add 4 to both sides of this equation to get 9x + 4 = 0<BR>\n" );
document.write( "9x + 4 is the factor.\r<BR>\n" );
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