Verified answer

Flip the second fraction and multiply.

x^3 - x / x^2 + 7x + 6 * 4x + 24 / x^2 - x

x(x+1)(x-1) / (x+6)(x+1) * 4(x+6) / x(x - 1)

x, (x+1)s, (x-1)s and (x+6)s cancel leaving just 4.

6/(x^2) + 7x - 1/x + x^3 + 95/4? That's all I got, a simplification.