Simplify the radical expression. state any restrictions on the variable

Hello from MrBillDoesMath!

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

The last choice shown ( t + 4; t <> 8)

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.

Step-by-step explanation:

b

step-by-step explanation:

b