How do you express (x^2 - 8x + 44) / ((x + 2) (x - 2)^2) in partial fractions?

1 Answer
Jan 2, 2018

(x^2-8x+44)/[(x+2)*(x-2)^2]=4/(x+2)-3/(x-2)+8/(x-2)^2

Explanation:

(x^2-8x+44)/[(x+2)*(x-2)^2]

=A/(x+2)+B/(x-2)+C/(x-2)^2

After expanding denominator,

A*(x-2)^2+B*(x^2-4)+C*(x+2)=x^2-8x+44

Set x=-2, 16A=64, so A=4

Set x=2, 4C=32, so C=8

Set x=0, 4A-4B+2C=44, so B=-3

Thus,

(x^2-8x+44)/[(x+2)*(x-2)^2]=4/(x+2)-3/(x-2)+8/(x-2)^2