Hello from MrBillDoesMath!
Answer:
The last choice shown ( t + 4; t <> 8)
Discussion:
The first thing to do is factor the numerator, t^2 - 4t -32. Now 4- 8 = -4 and 4(-8) = -32, suggesting that
t^2 -4t -32 = (t -8)(t+4)
Hence
(t^2 -4t -32) / (t -8) =
(t-8)(t+4) /(t-8) = => cancel (t-8) factor in both num and den.)
t+4
This is the last choice. Note that the above calculations assumed that x <> 8 as we are dividing by (t-8) and division by zero is not allowed.
Thank you,
MrB