document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=358027>Question 358027</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi Stuck on this question<BR>\n" );
document.write( "Express the following as a partial fraction\r<BR>\n" );
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document.write( "3x-1/x^2+4x+4\r<BR>\n" );
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document.write( "Really confuced here, i take it you factorise the equation to get \r<BR>\n" );
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document.write( "3x-1/(x+2)(x+2)\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #255577 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=255577\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "So far, so good.  But when you decompose partial fractions, if you have a factor squared in the original denominator, you have to represent the single factor in one denominator and the squared factor in another one, thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{3x\ -\ 1}{x^2\ +\ 4x\ +\ 4}\ =\ \frac{A}{x\ +\ 2}\ +\ \frac{B}{(x\ +\ 2)^2}\">\r<BR>\n" );
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document.write( "Apply the LCD in the RHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{3x\ -\ 1}{x^2\ +\ 4x\ +\ 4}\ =\ \frac{Ax\ +\ 2A\ +\ B}{(x\ +\ 2)^2}\">\r<BR>\n" );
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document.write( "Hence, equating the coefficients in the numerators:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ 3\">\r<BR>\n" );
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document.write( "And\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2A\ +\ B\ =\ -1\ \Rightarrow\ \ B\ =\ -7\">\r<BR>\n" );
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document.write( "Therefore:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{3x\ -\ 1}{x^2\ +\ 4x\ +\ 4}\ =\ \frac{3}{x\ +\ 2}\ -\ \frac{7}{(x\ +\ 2)^2}\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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