As with the numerical fractions, we have to put the rational functions over a common denominator by multiplying each by a clever form of 1. Once the denominators are the same, we can add the numerators.
We could continue to the next step, which would be
but we're not going to bother. We have the right form for the partial fractions technique when we get to the step
so we'll stop there.
When adding rational functions for the sake of the partial fractions technique, we don't multiply things out. For example, when adding
we stop here:
We also don't bother to write out the step where we multiply each fraction by a clever form of 1. We just multiply the numerator of each fraction by the denominator of the other fraction, then add the results.
If this doesn't make sense, we recommend reviewing how to add rational functions. If this does make sense, it's time to practice.