Partial fraction.
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1 Answer

(5x²+17x+15)/((x+2)²(x+1))=A/(x+2)+B/(x+2)²+C/(x+1).

5x²+17x+15=A(x+1)(x+2)+B(x+1)+C(x+2)².

5x²+17x+15=A(x²+3x+2)+B(x+1)+C(x²+4x+4).

Equating coefficients:

x²: A+C=5, C=5-A

x: 3A+B+4C=17=3A+B+20-4A, A-B=3, B=A-3

constant: 2A+B+4C=15=2A+A-3+20-4A=-A+17, A=2, B=-1, C=3.

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

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