Example 2

If st(c) = 4 and c ≠ 4, find

We note that the denominator has standard part 0,

st(c² - 16) = st(c)² — 16 = 4² - 16 = 0.

However, since c ≠ 4 the fraction is defined, and it can be simplified by factoring the numerator and denominator,

Then