If the fractions are complicated, there are ways to simplify them.
In many cases, we compute a sum or difference of fractions by finding
the common denominator. For instance,
14+1x=x4x+44x=x+44x,
and
1t−1t2+t=t+1t2+t−1t2+t=tt2+t=1t+1.
The following video shows how to use these sorts of manipulations to help
evaluate limits.