document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=983476>Question 983476</A>: <I><SPAN STYLE=\"word-break: break-all;\"> determine the partial fraction expansion of the rational functionh(x)= 1/(x-1)^2 (x^2+2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #604473 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=604473\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Including all needed parentheses,  h(x)= 1/((x-1)^2 (x^2+2))\r<BR>\n" );
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document.write( "Two constant variables for the linear denominator, and one linear variable expression for the quadratic denominator.<BR>\n" );
document.write( "The reason for two variables for the linear denominator is that this denominator occurs as factor twice  (see the exponent, \"2\").\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29=+1%2F%28%28x-1%29%5E2+%28x%5E2%2B2%29%29=A%2F%28x-1%29%2BB%2F%28x-1%29%5E2%2B%28Cx%2BD%29%2F%28x%5E2%2B2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Ignoring the h(x) member, multiply the other two members by the original denominator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=A%28x-1%29%28x%5E2%2B2%29%2BB%28x%5E2%2B2%29%2B%28Cx%2BD%29%28x-1%29 ALIGN=MIDDLE  ALT=\"1=A%28x-1%29%28x%5E2%2B2%29%2BB%28x%5E2%2B2%29%2B%28Cx%2BD%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Continue with the simplifications.\r<BR>\n" );
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document.write( "Most of the rest of the steps through....\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28x%5E3%2B2x-x%5E2-2%29%2BBx%5E2%2B2B%2BCx%5E2%2BDx-Cx-D ALIGN=MIDDLE  ALT=\"A%28x%5E3%2B2x-x%5E2-2%29%2BBx%5E2%2B2B%2BCx%5E2%2BDx-Cx-D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%5E3%2B2Ax-Ax%5E2-2%2BBx%5E2%2B2B%2BCx%5E2%2BDx-Cx-D ALIGN=MIDDLE  ALT=\"Ax%5E3%2B2Ax-Ax%5E2-2%2BBx%5E2%2B2B%2BCx%5E2%2BDx-Cx-D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%5E3%2B%28B%2BC-A%29x%5E2%2B%282A-C%2BD%29x%2B%282B-D%29 ALIGN=MIDDLE  ALT=\"Ax%5E3%2B%28B%2BC-A%29x%5E2%2B%282A-C%2BD%29x%2B%282B-D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Left member has only one constant term for an x^0 coefficient.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A=0%29 ALIGN=MIDDLE  ALT=\"highlight%28A=0%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=system%28A=0%2CB%2BC-A=0%2C2A-C%2BD=0%2C2B-D=1%29 ALIGN=MIDDLE  ALT=\"system%28A=0%2CB%2BC-A=0%2C2A-C%2BD=0%2C2B-D=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28B%2BC=0%2CC-D=0%2C2B-D=1%29 ALIGN=MIDDLE  ALT=\"system%28B%2BC=0%2CC-D=0%2C2B-D=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=D ALIGN=MIDDLE  ALT=\"C=D\"   DISABLED_style= \"max-width:90%; height:auto;\" >----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28B%2BC=0%2C2B-C=1%29 ALIGN=MIDDLE  ALT=\"system%28B%2BC=0%2C2B-C=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=2B ALIGN=MIDDLE  ALT=\"C=2B\"   DISABLED_style= \"max-width:90%; height:auto;\" >----useless.<BR>\n" );
document.write( "---<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-C ALIGN=MIDDLE  ALT=\"B=-C\"   DISABLED_style= \"max-width:90%; height:auto;\" >---<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28-C%29-C=1 ALIGN=MIDDLE  ALT=\"2%28-C%29-C=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2C-C=1 ALIGN=MIDDLE  ALT=\"-2C-C=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3C=1 ALIGN=MIDDLE  ALT=\"-3C=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28C=-%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"highlight%28C=-%281%2F3%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=B%2BC=0 ALIGN=MIDDLE  ALT=\"B%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=B=-C ALIGN=MIDDLE  ALT=\"B=-C\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28B=1%2F3%29 ALIGN=MIDDLE  ALT=\"highlight%28B=1%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Already determined C and D are equal.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28D=-%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"highlight%28D=-%281%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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