Question

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

Answer 1

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

Explanation:

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

The denominator `(x^2+4)` has no linear factors with Real coefficients since `x^2+4 >= 4 > 0` for all Real values of `x`.