You may want to review simplifying rational functions first.
As with fractions, it's easy to add or subtract rational functions with the same denominator. You just add or subtract the numerators, which are just polynomials. The denominator stays the same. For example, to compute (−x3 + 2x2)/(x2 − 1) − (−x2 − 1)/(x2 − 1), we just subtract the numerators, getting −x3 + 3x2 + 1. Then the answer is (−x3 + 3x2 + 1)/(x2 − 1). (We would have to reduce this, but the numerator and denominator have no factors in common, so there's nothing to reduce.)