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(x-1)/(x+1)(x-2)^2 = A/(x+1) + B/(x-2) + C/(x-2)^2
\n" ); document.write( "Multiply everything out with the common denominator of (x+1)(x-2)^2.\r
\n" ); document.write( "\n" ); document.write( "Then (x-1)/(x+1)(x-2)^2 = A(x-2)^2 + B(x+1)(x-2) + C((x+1)\r
\n" ); document.write( "\n" ); document.write( "Now make one of those parentheses on the right =0.
\n" ); document.write( "Let x=2
\n" ); document.write( "Then C(x+1)=x-1, if x=2 ;;; A and B both =0.
\n" ); document.write( "3C=1 ; c=(1/3)\r
\n" ); document.write( "\n" ); document.write( "Let x=-1
\n" ); document.write( "-2=9A
\n" ); document.write( "A=(-2/9)
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\n" ); document.write( "x=0
\n" ); document.write( "-1=4A-2B+C
\n" ); document.write( "but -1=(-8/9)-2B+1/3
\n" ); document.write( "-1=(-5/9)-2B
\n" ); document.write( "2B=4/9
\n" ); document.write( "B=2/9
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\n" ); document.write( "can check with a different x. Try 5
\n" ); document.write( "4=9*(-2/9)+18(2/9)+6(1/3)=-2+4+2=4, so it checks.\r
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\n" ); document.write( "It is -2/9(x+1) + 2/9(x-2)+ 1/3(x-2)^2\r
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