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Question

Resolve the fraction 2x2+2x+1x3+x2 into partial fraction.

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Solution

2x2+2x+1x3+x2=2x2+2x+1x2(x+1)=Ax+1+Bx+Cx2
A(x2)+Bx(x+1)+C(x+1)=2x2+2x+1
A+B=2,A+C=2,C=1A=1B=1
2x2+2x+1x3+x2=1x+1+1x+1x2

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