Question

What is the partial fraction decomposition of StartFraction 6 x + 17 Over (x + 1) squared EndFraction?

Answer 1

6/(x + 1) + 11/(x + 1)^2.

Explanation:

6x + 17 / (x +1)^2 = A / (x + 1) + B /(x + 1)^2

Multiply through by (x + 1)^2:

6x + 17 = A(x + 1) + B

Let x = -1, then:

-6 + 17 = 0 + b

So B = 11.

Let x = 1:

6 + 17 = A(1+1) + 11

23 = 2A + 11

A = (23-11)/ 2

A = 6.