document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180207>Question 1180207</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Decomposing fractions into partial fraction \r<BR>\n" );
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document.write( "x-2 /(x+2)^2(x-4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #809835 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=809835\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "By basic rules for decomposing fractions, the decomposition is of the form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%2F%28%28x%2B2%29%5E2%28x-4%29%29+=+A%2F%28x%2B2%29%2BB%2F%28x%2B2%29%5E2%2BC%2F%28x-4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Multiply by the least common denominator:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2=A%28x%2B2%29%28x-4%29%2BB%28x-4%29%2BC%28x%2B2%29%5E2 ALIGN=MIDDLE  ALT=\"x-2=A%28x%2B2%29%28x-4%29%2BB%28x-4%29%2BC%28x%2B2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2=A%28x%5E2-2x-8%29%2BB%28x-4%29%2BC%28x%5E2%2B4x%2B4%29 ALIGN=MIDDLE  ALT=\"x-2=A%28x%5E2-2x-8%29%2BB%28x-4%29%2BC%28x%5E2%2B4x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2=%28A%2BC%29x%5E2%2B%28-2A%2BB%2B4C%29x%2B%28-8A-4B%2B4C%29 ALIGN=MIDDLE  ALT=\"x-2=%28A%2BC%29x%5E2%2B%28-2A%2BB%2B4C%29x%2B%28-8A-4B%2B4C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Equate the coefficients on the two sides of the equation:<br><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2BC=0 ALIGN=MIDDLE  ALT=\"A%2BC=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2A%2BB%2B4C=1 ALIGN=MIDDLE  ALT=\"-2A%2BB%2B4C=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8A-4B%2B4C=-2 ALIGN=MIDDLE  ALT=\"-8A-4B%2B4C=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solve (1) to get C=-A and substitute in (2) and (3).<br><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6A%2BB=1 ALIGN=MIDDLE  ALT=\"-6A%2BB=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(5) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12A-4B=-2 ALIGN=MIDDLE  ALT=\"-12A-4B=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Eliminate A...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12A-2B=-2 ALIGN=MIDDLE  ALT=\"12A-2B=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12A-4B=-2 ALIGN=MIDDLE  ALT=\"-12A-4B=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6B=-4 ALIGN=MIDDLE  ALT=\"-6B=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=2%2F3 ALIGN=MIDDLE  ALT=\"B=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6A%2B2%2F3=1 ALIGN=MIDDLE  ALT=\"-6A%2B2%2F3=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6A=1%2F3 ALIGN=MIDDLE  ALT=\"-6A=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-1%2F18 ALIGN=MIDDLE  ALT=\"A=-1%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F18%2BC=0 ALIGN=MIDDLE  ALT=\"-1%2F18%2BC=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=1%2F18 ALIGN=MIDDLE  ALT=\"C=1%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%2F%28%28x%2B2%29%5E2%28x-4%29%29+=+%28-1%2F18%29%2F%28x%2B2%29%2B%282%2F3%29%2F%28x%2B2%29%5E2%2B%281%2F18%29%2F%28x-4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "or<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%2F%28%28x%2B2%29%5E2%28x-4%29%29+=+-1%2F%2818%28x%2B2%29%29%2B2%2F%283%28x%2B2%29%5E2%29%2B1%2F%2818%28x-4%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "-------------------------------------------------------------------------<br><BR>\n" );
document.write( "If you have more problems like this to do, you can check your answers on wolframalpha.com.  Just go to the website and enter e.g. \"decompose (x-2)/((x+2)^2(x-4))\".<br><BR>\n" );
document.write( " </SPAN>\n" );
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