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:

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.