Partial fraction decomposition

X^2-11x-18/x(x^2+ 3x + 3)
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(x^2-11x-18)/x(x^2+3x+3)=A/x+(Bx+C)/(x^2+3x+3). The quadratic doesn't factorise.

Ax^2+3Ax+3A+Bx^2+Cx=x^2-11x-18. Equating terms: 3A=-18, so A=-6; A+B=1, so B=7; 3A+C=-11, so C=-11+18=7.

Partial fractions are 7(x+1)/(x^2+3x+3)-6/x.

by Top Rated User (1.2m points)

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