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Question

Resolve 3x2+x2(x2)2(12x) into partial fractions.

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Solution

Assume 3x2+x2(x2)2(12x)=A12x+Bx2+C(x2)2;
3x2+x2=A(x2)2+B(12x)(x2)+C(12x)
Let 12x=0, then A=13;
Let x2=0, then C=4
To find B, equate the coefficients of x2, thus
3=A2Bl whence B=53
3x2+x2(x2)2(12x)=13(12x)53(x1)4(x2)2

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