document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=983639>Question 983639</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the partial fraction expansion of the rational function F(x)=X/x^2-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #604430 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=604430\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the partial fraction expansion of the rational function F(x)=X/x^2-1<BR>\n" );
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document.write( "x/(x^2-1) = a/(x-1) + b/(x+1)<BR>\n" );
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document.write( "[a(x+1) + b(x-1)]/(x^2-1)<BR>\n" );
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document.write( "Equate the numerators::<BR>\n" );
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document.write( "x = (a+b)x+(a-b)<BR>\n" );
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document.write( "Equations:<BR>\n" );
document.write( "a+b = 1<BR>\n" );
document.write( "a-b = 0<BR>\n" );
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document.write( "2a = 1<BR>\n" );
document.write( "a = 1/2<BR>\n" );
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document.write( "b = 1/2<BR>\n" );
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document.write( "Ans:: x/(x^2-1) = (1/2)/(x+1)+(1/2)/(x-1)<BR>\n" );
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document.write( "= 1/(2x+2) + 1/(2x-2)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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