Express the following as a sum of partial fractions 5x^2+17x+15\(x +2)^2(x+1)

Question

Partial fraction.

Answer 1

(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).