Question

How do you express `(3x+18)/(x^2+5x+4)` in partial fractions?

Answer 1

`(3x+18)/(x^2+5x+4)=5/(x+1)-2/(x+4)`

Explanation:

`(3x+18)/(x^2+5x+4)`

`=(3x+18)/((x+1)(x+4))`

`=A/(x+1)+B/(x+4)`

Use Heaviside's cover-up method to find:

`A = (3(-1)+18)/((-1)+4) = 15/3 = 5`

`B = (3(-4)+18)/((-4)+1) = 6/(-3) = -2`

So:

`(3x+18)/(x^2+5x+4)=5/(x+1)-2/(x+4)`