How do you simplify \frac { 4t - 16} { t ^ { 2} - 16}?

1 Answer
Nov 23, 2017

It simplifies to $\frac{4}{t + 4}$ when $t \ne \pm 4$.

Explanation:

Since $4 t - 16 = 4 \left(t - 4\right)$ and ${t}^{2} - 16 = \left(t - 4\right) \left(t + 4\right)$, we can say

$\frac{4 t - 16}{{t}^{2} - 16} = \frac{4 \left(t - 4\right)}{\left(t - 4\right) \left(t + 4\right)} = \frac{4 \left(\cancel{t - 4}\right)}{\left(\cancel{t - 4}\right) \left(t + 4\right)} = \frac{4}{t + 4}$.

This last expression is defined at $t = 4$ while the first expression is undefined at $t = 4$. Therefore this calculation is done under the assumption that $t \ne 4$.

Neither expression is defined at $t = - 4$, so this calculation also is done under the assumption that $t \ne - 4$.