Question

How do you express `((x^3+1)/(x^2+3))` in partial fractions?

Answer 1

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

Explanation:

`x^3+1=x(x^2+3)-3x+1`

Hence, `(x^3+1)/(x^2+3)=x+(-3x+1)/(x^2+3)` or `x-(3x-1)/(x^2+3)`

As `x^2+3` cannot be factorized, you cannot have further partial fractions.