If you look at limt→0(1t−1t2+t) or limx→−414+1x4+x
you will get the forms ∞−∞ and
00.
There are ways to simplify these fractions. For example, we
can change the form of the function that is a sum or difference of
fractions by finding a common denominator. For instance,
14+1x=x4x+44x=x+44x,
and 1t−1t2+t=t+1t2+t−1t2+t=tt2+t=1t+1( since t≠0).
These are
examples of how to do more work
when you get indeterminate forms ∞−∞
and 00 involving fractions.
The following video shows the details of evaluating these limits.