document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93247>Question 93247</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (x^2-9)/(2x-6) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #67884 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=67884\">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%5E2-9%29%2F%282x-6%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-9%29%2F%282x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that the numerator is the difference of two squares. As such it can be factored<BR>\n" );
document.write( "using the following rule:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2+-+B%5E2+=+%28A-B%29%2A%28A%2BB%29 ALIGN=MIDDLE  ALT=\"A%5E2+-+B%5E2+=+%28A-B%29%2A%28A%2BB%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This form is identical to the numerator in the given expression if you let A = x and B = 3.<BR>\n" );
document.write( "Substituting these into the rule you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+9%29+=+x%5E2+-+3%5E2+=+%28x-3%29%2A%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+9%29+=+x%5E2+-+3%5E2+=+%28x-3%29%2A%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So in place of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+9 ALIGN=MIDDLE  ALT=\"x%5E2+-+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > you can substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2A%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%2A%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to convert the given<BR>\n" );
document.write( "expression to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-3%29%2A%28x%2B3%29%29%2F%282x-6%29 ALIGN=MIDDLE  ALT=\"%28%28x-3%29%2A%28x%2B3%29%29%2F%282x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then notice that the denominator can be factored because 2 is common to both terms in<BR>\n" );
document.write( "the denominator. When you factor the 2 you then have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-3%29%2A%28x%2B3%29%29%2F%282%28x-3%29%29 ALIGN=MIDDLE  ALT=\"%28%28x-3%29%2A%28x%2B3%29%29%2F%282%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then you can cancel the term in the denominator that is common with the one in the numerator<BR>\n" );
document.write( "to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28cross%28x-3%29%29%2A%28x%2B3%29%29%2F%282%2A%28cross%28x-3%29%29%29 ALIGN=MIDDLE  ALT=\"%28%28cross%28x-3%29%29%2A%28x%2B3%29%29%2F%282%2A%28cross%28x-3%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and what remains is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%2F2 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is the answer to the problem.<BR>\n" );
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document.write( "Hope this helps you to understand a method for reducing the problem to a lower form. </SPAN>\n" );
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