Partial Fraction of the Rational Expression:

Question

x^2+x+8/x^3+x

Answer 1

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

So, you have

A/x + (Bx+C)/(x^2 + 1) = (x^2 + x + 8)/(x^3 + x)

Cross multiply and set coefficients equal to get

8/x + (1-7x)/(x^2+1)