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

1 Answer
Bill K.
Nov 23, 2017

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#.

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