Question

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

Answer 1

It simplifies to `4/(t+4)` when `t!=pm 4`.

Explanation:

Since `4t-16=4(t-4)` and `t^2-16=(t-4)(t+4)`, we can say

`(4t-16)/(t^2-16)=(4(t-4))/((t-4)(t+4))=(4(cancel(t-4)))/((cancel(t-4))(t+4))=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!=4`.

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