document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189175>Question 1189175</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify: (x / 2x^2-7x+3) - ((x-4) / (2x-1)(3-x)) - (7 / (x^2-x-6)) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820453 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=820453\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Let's factor the denominators and do a bit of tidying up.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+%28x-4%29%29+%2F%28%282x-1%29%28x-3%29%29+-+7+%2F+%28%28x-3%29%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"%28x+%2B+%28x-4%29%29+%2F%28%282x-1%29%28x-3%29%29+-+7+%2F+%28%28x-3%29%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "When focusing on the denominators, the unique factors are: (2x-1), (x-3), (x+2)<BR>\n" );
document.write( "The LCD is therefore (2x-1)(x-3)(x+2)<BR>\n" );
document.write( "Let's get each denominator to be equal to the LCD. That way we can add the fractions.\r<BR>\n" );
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document.write( "Answer: The original expression simplifies fully to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E2+-+14x-1+%29%2F+%282x%5E3-3x%5E2-11x%2B6%29 ALIGN=MIDDLE  ALT=\"%282x%5E2+-+14x-1+%29%2F+%282x%5E3-3x%5E2-11x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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