Question

How do you write the partial fraction decomposition of the rational expression `(x+4)/[(x+1)^2 + 4]`?

Answer 1

See explanation below

Explanation:

`(x+4)/((x+1)^2+4)=(x+4)/(x^2+2x+1+4)`

`=(x+4)/(x^2+2x+5)`

This cannot be decomposed into partial fractions as it is already in irreducible form.