document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=394712>Question 394712</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If we rewrite the expression 4/x(x-1)(x-2) in the form (A/x)+ (B/x-1) + (C/x-2)<BR>\n" );
document.write( "what are the values of A, B, and C? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #280055 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=280055\">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( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{4}{x(x\ -\ 1)(x\ -\ 2)}\ =\ \frac{A}{x}\ +\ \frac{B}{x\ -\ 1}\ +\ \frac{C}{x\ -\ 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{4}{x(x\ -\ 1)(x\ -\ 2)}\ =\ \frac{A(x\ -\ 1)(x\ -\ 2)\ +\ Bx(x\ -\ 2)\ +\ Cx(x\ -\ 1)}{x(x\ -\ 1)(x\ -\ 2)}\">\r<BR>\n" );
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document.write( "Expand the numerator in the RHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{4}{x(x\ -\ 1)(x\ -\ 2)}\ =\ \frac{Ax^2\ -\ 3Ax\ +\ 2A\ +\ Bx^2\ -\ 2Bx\ +\ Cx^2\ -\ Cx)}{x(x\ -\ 1)(x\ -\ 2)}\">\r<BR>\n" );
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document.write( "Combine like terms in the RHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{4}{x(x\ -\ 1)(x\ -\ 2)}\ =\ \frac{(A\ +\ B\ +\ C)x^2\ -\ (3A\ +\ 2B +\ C)x\ +\ 2A}{x(x\ -\ 1)(x\ -\ 2)}\">\r<BR>\n" );
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document.write( "Rewrite the numerator in the LHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{0x^2\ +\ 0x\ +\ 4}{x(x\ -\ 1)(x\ -\ 2)}\ =\ \frac{(A\ +\ B\ +\ C)x^2\ -\ (3A\ +\ 2B +\ C)x\ +\ 2A}{x(x\ -\ 1)(x\ -\ 2)}\">\r<BR>\n" );
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document.write( "Equate the coefficients:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A\ +\ B\ +\ C\ =\ 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -3A\ -\ 2B\ - C\ =\ 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2A\ =\ 4\">\r<BR>\n" );
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document.write( "Solve the system for A, B, and C\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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