document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=86680>Question 86680</A>: <I><SPAN STYLE=\"word-break: break-all;\"> add or subtract as indicated.     x/x+4-36/x^2-x-20 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #62746 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=62746\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F%28x%2B4%29%29-%2836%2F%28x%5E2-x-20%29%29 ALIGN=MIDDLE  ALT=\"%28x%2F%28x%2B4%29%29-%2836%2F%28x%5E2-x-20%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract<BR>\n" );
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document.write( "Notice first that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x-20 ALIGN=MIDDLE  ALT=\"x%5E2-x-20\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B4%29%2A%28x+-5%29 ALIGN=MIDDLE  ALT=\"%28x+%2B4%29%2A%28x+-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute the factored<BR>\n" );
document.write( "form into the problem, and the problem becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F%28x%2B4%29%29-%2836%2F%28%28x%2B4%29%2A%28x-5%29%29%29%29 ALIGN=MIDDLE  ALT=\"%28x%2F%28x%2B4%29%29-%2836%2F%28%28x%2B4%29%2A%28x-5%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next, create a common denominator in the two terms by multiplying the first term by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%2F%28x-5%29 ALIGN=MIDDLE  ALT=\"%28x-5%29%2F%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is equivalent to multiplying by 1 because the numerator of this <BR>\n" );
document.write( "multiplier is the same as the denominator.  This multiplication makes the problem <BR>\n" );
document.write( "become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F%28x%2B4%29%29%2A%28%28x-5%29%2F%28x-5%29%29-%2836%2F%28%28x%2B4%29%2A%28x-5%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and this simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2A%28x-5%29%29%2F%28%28x%2B4%29%2A%28x-5%29%29%29-%2836%2F%28%28x%2B4%29%2A%28x-5%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The numerator of the first term multiplies out to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x ALIGN=MIDDLE  ALT=\"x%5E2-5x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substituting this into<BR>\n" );
document.write( "the polynomial makes it become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2+-+5x%29%2F%28%28x%2B4%29%2A%28x-5%29%29%29-%2836%2F%28%28x%2B4%29%2A%28x-5%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now since the two terms have the same denominator, they can be combined by just subtracting<BR>\n" );
document.write( "the two numerators and putting that result over the common denominator.  This results<BR>\n" );
document.write( "in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2+-+5x+-36%29%2F%28%28x%2B4%29%2A%28x-5%29%29%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%5E2+-+5x+-36%29%2F%28%28x%2B4%29%2A%28x-5%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now notice that the numerator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+5x+-+36 ALIGN=MIDDLE  ALT=\"x%5E2+-+5x+-+36\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+9%29%2A%28x+%2B+4%29 ALIGN=MIDDLE  ALT=\"%28x+-+9%29%2A%28x+%2B+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Substitute this for the numerator and the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28x-9%29%2A%28x%2B4%29%29%29%2F%28%28x%2B4%29%2A%28x-5%29%29%29%29 ALIGN=MIDDLE  ALT=\"%28%28%28x-9%29%2A%28x%2B4%29%29%29%2F%28%28x%2B4%29%2A%28x-5%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Cancel the like terms in the numerator and denominator:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28x-9%29%2A%28cross%28x%2B4%29%29%29%29%2F%28%28cross%28x%2B4%29%29%2A%28x-5%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and this reduces to the form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-9%29%2F%28x-5%29 ALIGN=MIDDLE  ALT=\"%28x-9%29%2F%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is the answer you are looking for. Hope this helps you to understand the problem<BR>\n" );
document.write( "and how to work it through to an answer.<BR>\n" );
document.write( ". </SPAN>\n" );
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