You may want to review the case with a common denominator and finding common denominators first.

If the two rational functions you want to add or subtract don't
have a common denominator, you need to rewrite them so they do,
just as with fractions. For example, if you have to subtract
(*x* + 1)/(*x* − 1) − *x*, the common
denominator is *x* − 1. We need to rewrite *x* so
it has this denominator too, so we write it as *x*(*x*
− 1)/(*x* − 1) = (*x*^{2}
− *x*)/(*x* − 1). Now subtracting gives us
(−*x*^{2} + 2*x* + 1)/(*x* −
1). Finally, we look for common factors of the numerator and
denominator to reduce; there aren't any, so we're done.