Question

Resolve into partial fractions:

(x+3)(x+1)/
x(x^2+x+1)

Can anyone please help me out?

Answer 1

8/x^3

Answer 2

(x+3)(x+1)/[x(x^2+x+1)] =

A/x + (B + C x)/(x^2 + x + 1)


To find A multiply both sides by x and take the limit x --> 0:

A = 3

To find B and C you can just move the A/x term to the other side and simplify:

(B + C x)/(x^2 + x + 1) =

(x+3)(x+1)/[x(x^2+x+1)] - 3/x =

(x^2 + 4x + 3 - 3 x^2 - 3 x - 3)/[x(x^2+x+1)] =

(-2x^2 + x)/[x(x^2+x+1)] =

(1 - 2x)/(x^2+x+1)