document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=216079>Question 216079</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (x-6x+9)/(x-3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #163206 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=163206\">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=%28x%5E2-6x%2B9%29%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-6x%2B9%29%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 1.  Look at the numerator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B9 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Step 2.  Need to integers m and n whose sum is -6 and product is 9.\r<BR>\n" );
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document.write( "Step 3.  The two integers are -3 and -3.  We can factor through grouping where -6x=-3x-3x.  We can also recognize that the trinomial is a perfect square, that is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B9=%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B9=%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Nevertheless the following steps, will show the technique of grouping.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B9=%28x%5E2-3x%29%2B%28-3x%2B9%29=x%28x-3%29-3%28x-3%29 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B9=%28x%5E2-3x%29%2B%28-3x%2B9%29=x%28x-3%29-3%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Factor (x-3) from both groups\r<BR>\n" );
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document.write( "Step 4.  Now substitute the expression in Step 3 with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2\"   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=%28x%5E2-6x%2B9%29%2F%28x-3%29=%28x-3%29%5E2%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-6x%2B9%29%2F%28x-3%29=%28x-3%29%5E2%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note we can cancel the factor (x-3) in the numerator and denominator.\r<BR>\n" );
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document.write( "Step 4.  ANSWER:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-6x%2B9%29%2F%28x-3%29=x-3 ALIGN=MIDDLE  ALT=\"%28x%5E2-6x%2B9%29%2F%28x-3%29=x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I hope the above steps were helpful. \r<BR>\n" );
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document.write( "For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "And good luck in your studies!\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J<BR>\n" );
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