x^2 / (x^3-8)
Once you have factored the denominator completely, set up your new fractions:
For every linear factor include the term . If you have powers of the same factor, , include all of the terms .
For each quadratic factor (or power of a quadratic factor), , include all of the terms .
So, in this case we have
So, we have
Multiply through by :
Collect terms of the same degree, and equate the coefficients of both sides. Can you finish?