document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=22911>Question 22911</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ((x)/(x-4)-(2)/(x+3))/((x^2-4x)/(2x+6))<BR>\n" );
document.write( "These problems are giving me a hard time I know you have to get a common denominator and everything but for some reason i get stuck. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #11475 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=11475\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First of all, congratulations on getting all the parentheses in the right place in typing this problem.  If you put 3 sets of set braces before and 3 after this, then your question will be expressed in perfect form for a complex fraction:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28x%29%2F%28x-4%29-%282%29%2F%28x%2B3%29%29%2F%28%28x%5E2-4x%29%2F%282x%2B6%29%29 ALIGN=MIDDLE  ALT=\"+%28%28x%29%2F%28x-4%29-%282%29%2F%28x%2B3%29%29%2F%28%28x%5E2-4x%29%2F%282x%2B6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's just \"unstack\" the problem and write it like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28x%29%2F%28x-4%29-%282%29%2F%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"+%28%28x%29%2F%28x-4%29-%282%29%2F%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2-4x%29%2F%282x%2B6%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%5E2-4x%29%2F%282x%2B6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "On the left side, you need to find a common denominator, which is (x-4)(x+3).  Multiply the first fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%2F%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the second fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%2F%28X-4%29 ALIGN=MIDDLE  ALT=\"%28x-4%29%2F%28X-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  It should look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28%28x%29%2F%28x-4%29%29%2A%28%28x%2B3%29%2F%28x%2B3%29%29-%28%282%29%2F%28x%2B3%29%29%2A%28%28x-4%29%2F%28x-4%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2-4x%29%2F%282x%2B6%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%5E2-4x%29%2F%282x%2B6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, put down the common denominator for the first fraction; combine numerators to form the first numerator, and invert and factor the second fraction:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E2%2B3x+-2x%2B8%29%2F%28%28x-4%29%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"+%28x%5E2%2B3x+-2x%2B8%29%2F%28%28x-4%29%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28x%2B3%29%29%2F+%28x%28x-4%29%29++ ALIGN=MIDDLE  ALT=\"%282%28x%2B3%29%29%2F+%28x%28x-4%29%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Combine like terms in the first numerator, divide out the (x+3) factors in the first denominator and the second numerator:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E2%2Bx+%2B8%29%2F%28x-4%29 ALIGN=MIDDLE  ALT=\"+%28x%5E2%2Bx+%2B8%29%2F%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F+%28x%28x-4%29%29++ ALIGN=MIDDLE  ALT=\"2%2F+%28x%28x-4%29%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This brings (I hope!!) the final answer:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282%2A%28x%5E2%2Bx+%2B8%29%29%2F%28x%2A%28x-4%29%5E2%29 ALIGN=MIDDLE  ALT=\"+%282%2A%28x%5E2%2Bx+%2B8%29%29%2F%28x%2A%28x-4%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "R^2 at SCC\r<BR>\n" );
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document.write( "P.S.  That was ugly!!  Somebody let me know if there might be an error in all of that!!\r<BR>\n" );
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document.write( " </SPAN>\n" );
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