document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=155251>Question 155251</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a student was given the problem 4x^2-9 divided by 6x-9<BR>\n" );
document.write( "                               -------<BR>\n" );
document.write( "                               4x^2+12x+9\r<BR>\n" );
document.write( "\n" );
document.write( "He answer is 3(2x-3). Is it correct, why. And if not how would you suggest he solve the problem? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #114307 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=114307\">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=%28%284x%5E2-9%29%2F%286x-9%29%29%2F%284x%5E2%2B12x%2B9%29 ALIGN=MIDDLE  ALT=\"%28%284x%5E2-9%29%2F%286x-9%29%29%2F%284x%5E2%2B12x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284x%5E2-9%29%2F%286x-9%29%29%2F%28%284x%5E2%2B12x%2B9%29%2F1%29 ALIGN=MIDDLE  ALT=\"%28%284x%5E2-9%29%2F%286x-9%29%29%2F%28%284x%5E2%2B12x%2B9%29%2F1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <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;\" > as a fraction by adding a denominator of 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284x%5E2-9%29%2F%286x-9%29%29%2A%281%2F%284x%5E2%2B12x%2B9%29%29 ALIGN=MIDDLE  ALT=\"%28%284x%5E2-9%29%2F%286x-9%29%29%2A%281%2F%284x%5E2%2B12x%2B9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the top-most fraction by the reciprocal of the bottom-most fraction\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%282x%2B3%29%282x-3%29%29%2F%286x-9%29%29%2A%281%2F%284x%5E2%2B12x%2B9%29%29 ALIGN=MIDDLE  ALT=\"%28%28%282x%2B3%29%282x-3%29%29%2F%286x-9%29%29%2A%281%2F%284x%5E2%2B12x%2B9%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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%282x%2B3%29%282x-3%29%29%2F%283%282x-3%29%29%29%2A%281%2F%284x%5E2%2B12x%2B9%29%29 ALIGN=MIDDLE  ALT=\"%28%28%282x%2B3%29%282x-3%29%29%2F%283%282x-3%29%29%29%2A%281%2F%284x%5E2%2B12x%2B9%29%29\"   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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%282x%2B3%29%282x-3%29%29%2F%283%282x-3%29%29%29%2A%281%2F%28%282x%2B3%29%282x%2B3%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=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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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-3%29%282x%2B3%29%282x%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28%282x%2B3%29%282x-3%29%29%2F%283%282x-3%29%282x%2B3%29%282x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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%283%2Ahighlight%28%282x-3%29%29highlight%28%282x%2B3%29%29%282x%2B3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Highlight the common terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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%283%2Across%28%282x-3%29%29cross%28%282x%2B3%29%29%282x%2B3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out the common terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284x%5E2-9%29%2F%286x-9%29%29%2F%284x%5E2%2B12x%2B9%29 ALIGN=MIDDLE  ALT=\"%28%284x%5E2-9%29%2F%286x-9%29%29%2F%284x%5E2%2B12x%2B9%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;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284x%5E2-9%29%2F%286x-9%29%29%2F%284x%5E2%2B12x%2B9%29=1%2F%283%282x%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28%284x%5E2-9%29%2F%286x-9%29%29%2F%284x%5E2%2B12x%2B9%29=1%2F%283%282x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-3%2F2 ALIGN=MIDDLE  ALT=\"x%3C%3E-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E3%2F2 ALIGN=MIDDLE  ALT=\"x%3C%3E3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So his answer is incorrect. In the future, I would suggest checking the answer. You can check the answer by graphing the original expression and comparing it to the graph of the answer. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );