document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=951325>Question 951325</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I'm struggling with this question and would really appreciate some help;\r<BR>\n" );
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document.write( "In the partial fraction solution, \r<BR>\n" );
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document.write( "(x-3)/x(x^2+3) = a/x + (bx + c) /(x^2+3) \r<BR>\n" );
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document.write( "What are the values of a, b and c? \r<BR>\n" );
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document.write( "I'm multiplying through to compare coefficients but end up an x^2 term, or splitting the original fraction treating it as having distinct linear factors and then getting an x cubed term \r<BR>\n" );
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document.write( "Thanks for your help, <BR>\n" );
document.write( "Rob  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #580922 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=580922\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fx+%2B+%28bx+%2B+c%29+%2F%28x%5E2%2B3%29 ALIGN=MIDDLE  ALT=\"a%2Fx+%2B+%28bx+%2B+c%29+%2F%28x%5E2%2B3%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=%28a%2Fx%29%28%28x%5E2%2B3%29%2F%28x%5E2%2B3%29%29%2B%28%28bx%2Bc%29%2F%28x%5E2%2B3%29%29%28x%2Fx%29 ALIGN=MIDDLE   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=%28a%28x%5E2%2B3%29%2Bx%28bx%2Bc%29%29%2F%28x%28x%5E2%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28a%28x%5E2%2B3%29%2Bx%28bx%2Bc%29%29%2F%28x%28x%5E2%2B3%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=%28ax%5E2%2B3a%2Bbx%5E2%2Bcx%29%2F%28x%28x%5E2%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28ax%5E2%2B3a%2Bbx%5E2%2Bcx%29%2F%28x%28x%5E2%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Yes, a squared term should occur.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283a%2Bcx%2B%28a%2Bb%29x%5E2%29%2F%28x%28x%5E2%2B3%29%29 ALIGN=MIDDLE  ALT=\"%283a%2Bcx%2B%28a%2Bb%29x%5E2%29%2F%28x%28x%5E2%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now comparing the numerator expressions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=3a%2Bcx%2B%28a%2Bb%29x%5E2 ALIGN=MIDDLE  ALT=\"x-3=3a%2Bcx%2B%28a%2Bb%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=%28a%2Bb%29x%5E2%2Bcx%2B3a ALIGN=MIDDLE  ALT=\"x-3=%28a%2Bb%29x%5E2%2Bcx%2B3a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equations for the coefficients should give a system,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a%2Bb=0%2C1=c%2C-3=3a%29 ALIGN=MIDDLE  ALT=\"system%28a%2Bb=0%2C1=c%2C-3=3a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The last equation in the system means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=-1%29 ALIGN=MIDDLE  ALT=\"highlight%28a=-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >;  therefore using the first in the system, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b=1%29 ALIGN=MIDDLE  ALT=\"highlight%28b=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The other equation is simply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=1%29 ALIGN=MIDDLE  ALT=\"highlight%28c=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The decomposed fraction should be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28-1%2Fx%2B%28x%2B1%29%2F%28x%5E2%2B3%29%29 ALIGN=MIDDLE  ALT=\"highlight%28-1%2Fx%2B%28x%2B1%29%2F%28x%5E2%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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