document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73725>Question 73725</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a^2-9/a^2+5a+6. simplify </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52744 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=52744\">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=%28a%5E2-9%29%2F%28a%5E2%2B5a%2B6%29 ALIGN=MIDDLE  ALT=\"%28a%5E2-9%29%2F%28a%5E2%2B5a%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The numerator of this fraction is the difference of two squares.  Therefore, it factors into<BR>\n" );
document.write( "the product of the sum and the difference of the square root of both terms.  Sounds tough<BR>\n" );
document.write( "but all it says is that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E2+-+9%29=+%28sqrt%28a%5E2%29-sqrt%289%29%29%2A%28sqrt%28a%5E2%29+%2B+sqrt%289%29%29=%28a+-3%29%2A%28a%2B3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now you need to factor the denominator of the problem.  Because this is a \"set up practice\"<BR>\n" );
document.write( "problem you can presume that it will factor and that either (a-3) or (a+3) is likely to<BR>\n" );
document.write( "be one of the factors.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E2+%2B+5a+%2B+6%29 ALIGN=MIDDLE  ALT=\"%28a%5E2+%2B+5a+%2B+6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > needs to be factored.  The first term in each of the factors will be \"a\" and<BR>\n" );
document.write( "the second term will have to be factors of 6 ... 6 and 1 or 3 and 2. 3 and 2 look good <BR>\n" );
document.write( "because they add up to be 5 and (+3)*(+2) = +6.<BR>\n" );
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document.write( "So the factors of are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E2+%2B+5a+%2B+6%29=%28a%2B3%29%2A%28a%2B2%29 ALIGN=MIDDLE  ALT=\"%28a%5E2+%2B+5a+%2B+6%29=%28a%2B3%29%2A%28a%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can verify this by multiplying (a+3)*(a+2) and look at the result.<BR>\n" );
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document.write( "Substituting the factors back into the original fraction result in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28a+-3%29%2A%28a%2B3%29%29%2F%28%28a%2B3%29%2A%28a%2B2%29%29 ALIGN=MIDDLE  ALT=\"+%28%28a+-3%29%2A%28a%2B3%29%29%2F%28%28a%2B3%29%2A%28a%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Cancel the (a+3) terms that are common 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%28a+-3%29%2Across%28a%2B3%29%29%2F%28cross%28a%2B3%29%2A%28a%2B2%29%29 ALIGN=MIDDLE  ALT=\"+%28%28a+-3%29%2Across%28a%2B3%29%29%2F%28cross%28a%2B3%29%2A%28a%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and the final answer is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-3%29%2F%28a%2B2%29 ALIGN=MIDDLE  ALT=\"%28a-3%29%2F%28a%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you see the value of using factors to simplify problems such as these. </SPAN>\n" );
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