document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=77996>Question 77996</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation:\r<BR>\n" );
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document.write( "(15x^3-10x^2) over (3x^2-5x+2)\r<BR>\n" );
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document.write( "I have no idea how to solve this so I can't provide any work that proves that I have tried doing it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #55890 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=55890\">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=%2815x%5E3-10x%5E2%29%2F%283x%5E2-5x%2B2%29 ALIGN=MIDDLE  ALT=\"%2815x%5E3-10x%5E2%29%2F%283x%5E2-5x%2B2%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=%285x%5E2%283x-2%29%29%2F%283x%5E2-5x%2B2%29 ALIGN=MIDDLE  ALT=\"%285x%5E2%283x-2%29%29%2F%283x%5E2-5x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out 5x^2 on the numerator\r<BR>\n" );
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document.write( "Now factor the denominator:\r<BR>\n" );
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document.write( "ERROR Algebra::Solver::Engine::invoke_solver_noengine: solver not defined for name 'quadratic_factoring'.\n" );
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document.write( " <TR><TD >Error occurred executing solver 'quadratic_factoring' .</TD></TR>\n" );
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document.write( "So we get the expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%5E2%283x-2%29%29%2F%28%283x-2%29%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%285x%5E2%283x-2%29%29%2F%28%283x-2%29%28x-1%29%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=%285x%5E2cross%28%283x-2%29%29%29%2F%28cross%28%283x-2%29%29%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%285x%5E2cross%28%283x-2%29%29%29%2F%28cross%28%283x-2%29%29%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Notice the terms <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2 ALIGN=MIDDLE  ALT=\"3x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > cancel\r<BR>\n" );
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document.write( "which leaves us with this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%5E2%29%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"%285x%5E2%29%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815x%5E3-10x%5E2%29%2F%283x%5E2-5x%2B2%29 ALIGN=MIDDLE  ALT=\"%2815x%5E3-10x%5E2%29%2F%283x%5E2-5x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > reduces to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%5E2%29%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"%285x%5E2%29%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "As always, you can graph the two expressions as equations and they will be the same. This means they are equivalent. </SPAN>\n" );
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