document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=156524>Question 156524</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My teacher gave this problem \r<BR>\n" );
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document.write( "    4x^-9  <BR>\n" );
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document.write( "   4x^2+12x+9  divided by  6x-9\r<BR>\n" );
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document.write( "I got 3(2x+3), my teacher said I was wrong.Please help me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #115296 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=115296\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Is the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284x%5E2-9%29%2F%284x%5E2%2B12x%2B9%29%29%2F%286x-9%29 ALIGN=MIDDLE  ALT=\"%28%284x%5E2-9%29%2F%284x%5E2%2B12x%2B9%29%29%2F%286x-9%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=%28%284x%5E2-9%29%2F%284x%5E2%2B12x%2B9%29%29%2F%286x-9%29 ALIGN=MIDDLE  ALT=\"%28%284x%5E2-9%29%2F%284x%5E2%2B12x%2B9%29%29%2F%286x-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284x%5E2-9%29%2F%284x%5E2%2B12x%2B9%29%29%2F%28%286x-9%29%2F1%29 ALIGN=MIDDLE  ALT=\"%28%284x%5E2-9%29%2F%284x%5E2%2B12x%2B9%29%29%2F%28%286x-9%29%2F1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-9 ALIGN=MIDDLE  ALT=\"6x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x-9%29%2F1 ALIGN=MIDDLE  ALT=\"%286x-9%29%2F1\"   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=%28%284x%5E2-9%29%2F%284x%5E2%2B12x%2B9%29%29%2A%281%2F%286x-9%29%29 ALIGN=MIDDLE  ALT=\"%28%284x%5E2-9%29%2F%284x%5E2%2B12x%2B9%29%29%2A%281%2F%286x-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the first fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E2-9%29%2F%284x%5E2%2B12x%2B9%29 ALIGN=MIDDLE  ALT=\"%284x%5E2-9%29%2F%284x%5E2%2B12x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by the reciprocal of the second fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x-9%29%2F1 ALIGN=MIDDLE  ALT=\"%286x-9%29%2F1\"   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=%28%28%282x%2B3%29%282x-3%29%29%2F%284x%5E2%2B12x%2B9%29%29%2A%281%2F%286x-9%29%29 ALIGN=MIDDLE  ALT=\"%28%28%282x%2B3%29%282x-3%29%29%2F%284x%5E2%2B12x%2B9%29%29%2A%281%2F%286x-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-9 ALIGN=MIDDLE  ALT=\"4x%5E2-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B3%29%282x-3%29 ALIGN=MIDDLE  ALT=\"%282x%2B3%29%282x-3%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=%28%28%282x%2B3%29%282x-3%29%29%2F%28%282x%2B3%29%282x%2B3%29%29%29%2A%281%2F%286x-9%29%29 ALIGN=MIDDLE  ALT=\"%28%28%282x%2B3%29%282x-3%29%29%2F%28%282x%2B3%29%282x%2B3%29%29%29%2A%281%2F%286x-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B12x%2B9 ALIGN=MIDDLE  ALT=\"4x%5E2%2B12x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B3%29%282x%2B3%29 ALIGN=MIDDLE  ALT=\"%282x%2B3%29%282x%2B3%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=%28%28%282x%2B3%29%282x-3%29%29%2F%28%282x%2B3%29%282x%2B3%29%29%29%2A%281%2F%283%282x-3%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-9 ALIGN=MIDDLE  ALT=\"6x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%282x-3%29 ALIGN=MIDDLE  ALT=\"3%282x-3%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=%28%282x%2B3%29%282x-3%29%29%2F%283%282x%2B3%29%282x%2B3%29%282x-3%29%29 ALIGN=MIDDLE  ALT=\"%28%282x%2B3%29%282x-3%29%29%2F%283%282x%2B3%29%282x%2B3%29%282x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%28%282x%2B3%29%29highlight%28%282x-3%29%29%29%2F%283highlight%28%282x%2B3%29%29%282x%2B3%29highlight%28%282x-3%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  Highlight the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%28%282x%2B3%29%29cross%28%282x-3%29%29%29%2F%283cross%28%282x%2B3%29%29%282x%2B3%29cross%28%282x-3%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  Cancel out the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%283%282x%2B3%29%29 ALIGN=MIDDLE  ALT=\"1%2F%283%282x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%286x%2B9%29 ALIGN=MIDDLE  ALT=\"1%2F%286x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute (this step is optional)\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284x%5E2-9%29%2F%284x%5E2%2B12x%2B9%29%29%2F%286x-9%29 ALIGN=MIDDLE  ALT=\"%28%284x%5E2-9%29%2F%284x%5E2%2B12x%2B9%29%29%2F%286x-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%283%282x%2B3%29%29 ALIGN=MIDDLE  ALT=\"1%2F%283%282x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%286x%2B9%29 ALIGN=MIDDLE  ALT=\"1%2F%286x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Note: you can use a graph to verify your answer. Simply graph the original expression and the answer. If the two graphs are identical (which in this case they are), then this shows that the two expressions are equivalent and it verifies the answer. </SPAN>\n" );
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