document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1059713>Question 1059713</A>: <I><SPAN STYLE=\"word-break: break-all;\"> rewrite the rational expression as an equivalent rational expression with the given denominator\r<BR>\n" );
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document.write( "x/x^3+7x^2+12x=?/x(x+5)(x+3)(x+4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #674751 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=674751\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3>Let's factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B7x%5E2%2B12x ALIGN=MIDDLE  ALT=\"x%5E3%2B7x%5E2%2B12x\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is the denominator on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%5E2%2B7x%2B12%29 ALIGN=MIDDLE  ALT=\"x%28x%5E2%2B7x%2B12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B3%29%28x%2B4%29 ALIGN=MIDDLE  ALT=\"x%28x%2B3%29%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Looking at that factorization and comparing it to x(x+5)(x+3)(x+4), which is the denominator on the right side, all we're missing is (x+5).\r<BR>\n" );
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document.write( "So multiply top and bottom of the fraction on the left by (x+5) to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x%5E3%2B7x%5E2%2B12x%29+=+x%2F%28x%28x%2B3%29%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"x%2F%28x%5E3%2B7x%5E2%2B12x%29+=+x%2F%28x%28x%2B3%29%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x%5E3%2B7x%5E2%2B12x%29+=+%28x%2Ahighlight%28%28x%2B5%29%29%29%2F%28x%28x%2B3%29%28x%2B4%29%2Ahighlight%28%28x%2B5%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x%5E3%2B7x%5E2%2B12x%29+=+%28x%28x%2B5%29%29%2F%28x%28x%2B5%29%28x%2B3%29%28x%2B4%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means that <font color=red>x(x+5)</font> will go where the question mark is. </font> </SPAN>\n" );
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