document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117478>Question 117478</A>: <I><SPAN STYLE=\"word-break: break-all;\"> decompose into a partial fraction\r<BR>\n" );
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document.write( "2x^3+x^2-3x+5 / x^2-2x-3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85998 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=85998\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Decompose into a partial fraction<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E3%2Bx%5E2-3x%2B5%29+%2F+%28x%5E2-2x-3%29 ALIGN=MIDDLE  ALT=\"%282x%5E3%2Bx%5E2-3x%2B5%29+%2F+%28x%5E2-2x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Numerator degree is greater than the denominator:<BR>\n" );
document.write( "Divide using long division:<BR>\n" );
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document.write( "(x^2-2x-3)|2x^3 + x^2 - 3x+ 5<BR>\n" );
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document.write( "You should get 2x + 5:  + Remainder<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2813x%2B20%29%2F%28x%5E2-2x-3%29 ALIGN=MIDDLE  ALT=\"%2813x%2B20%29%2F%28x%5E2-2x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Decompose the remainder:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2813x%2B20%29%2F%28x%5E2-2x-3%29 ALIGN=MIDDLE  ALT=\"%2813x%2B20%29%2F%28x%5E2-2x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor the denominator<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2813x%2B20%29+%2F%28%28x-3%29%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"%2813x%2B20%29+%2F%28%28x-3%29%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F%28%28x-3%29%29 ALIGN=MIDDLE  ALT=\"A%2F%28%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%2F%28%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"B%2F%28%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A%28x%2B1%29+%2B+B%28x-3%29%29%2F%28%28x-3%29%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28A%28x%2B1%29+%2B+B%28x-3%29%29%2F%28%28x-3%29%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since these fractions have the same denominator, their numerators have to be equal<BR>\n" );
document.write( "13x+20 = A(x+1) + B(x-3) <BR>\n" );
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document.write( "Let x = 3, then  B drops out and we can solve for A:<BR>\n" );
document.write( "13(3) + 20 = A(3+1) + B(3-3) <BR>\n" );
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document.write( "39 + 20= A(4) + B(0)<BR>\n" );
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document.write( "59 = 4A<BR>\n" );
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document.write( "A = 59/4<BR>\n" );
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document.write( "A = 14.75<BR>\n" );
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document.write( "Let x = -1, then A drops out<BR>\n" );
document.write( "13(-1) + 20 = A(-1+1) + B(-1-3)<BR>\n" );
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document.write( "-13 + 20 = A(0) + B(-4)<BR>\n" );
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document.write( "7 = -4B<BR>\n" );
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document.write( "B = 7/-4<BR>\n" );
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document.write( "B = -1.75<BR>\n" );
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document.write( "The quotient and the partial fractions:<BR>\n" );
document.write( "(2x + 5) + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14.75%2F%28%28x-3%29%29 ALIGN=MIDDLE  ALT=\"14.75%2F%28%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1.75%29%2F%28%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28-1.75%29%2F%28%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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