document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1031246>Question 1031246</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the partial decomposition of the rational expression:\r<BR>\n" );
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document.write( "(-x^2+2x+4)/(x(x+2)^2) = A/x + B/(x+2) + C/(x+2)^2\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #646001 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=646001\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write the partial decomposition of the rational expression: <BR>\n" );
document.write( "(-x^2+2x+4)/(x(x+2)^2) = A/x + B/(x+2) + C/(x+2)^2 <BR>\n" );
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document.write( "Equate the numerators since the denominators are the same.<BR>\n" );
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document.write( "-x^2 + 2x + 4 = A(x+2)^2 + Bx(x+2) + Cx<BR>\n" );
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document.write( "-x^2 + 2x + 4 = Ax^2 + 4Ax + 4A + Bx^2 + 2Bx + Cx<BR>\n" );
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document.write( "-x^2 + 2x + 4 = (A+B)x^2 + (4A + 2B + C)x + 4A<BR>\n" );
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document.write( "Equate corresponding coefficients::<BR>\n" );
document.write( "A+B = -1<BR>\n" );
document.write( "4A + 2B + C = 2<BR>\n" );
document.write( "4A = 4<BR>\n" );
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document.write( "A = 1<BR>\n" );
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document.write( "So, B = -2<BR>\n" );
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document.write( "And C = 2-4+4 = 2<BR>\n" );
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document.write( "Ans: 1/x - 2/(x+2) + 2/(x+2)^2<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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