How do you simplify \frac { 4t - 16} { t ^ { 2} - 16}4t16t216?

1 Answer
Nov 23, 2017

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

Explanation:

Since 4t-16=4(t-4)4t16=4(t4) and t^2-16=(t-4)(t+4)t216=(t4)(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.