Question

Simplify the rational expression. State any restrictions on the variable.

t^2-4t-32/t-8

a. -t - 4; t = 8
b. -t + 4; t = -8
c. t + 4; t = 8

Answer 1

(C)t+4; t=8

Explanation:

The given rational expression is:

`(t^2-4t-32)/(t-8)`

Simplifying the above expression, we get

=
`(t^2-8t+4t-32)/(t-8)`

=
`(t(t-8)+4(t-8))/(t-8)`

=
`((t+4)(t-8))/((t-8))`

=
`t+4`

which is the required simplified form of the given expression.

And the restrictions on the given expression is t=8, because when we substitute t=8 in the expression, it becomes infinite.

Thus, option C is correct.

Answer 2

t^2-4t-32= 0, implies sqrtDelta = 6
so t = 2 - 6= -4, or t = 2+6= 8
so t^2-4t-32/t-8 = (t + 4) (t-8) / t-8 = t+4, it is the simplified form
so the answer is c. t + 4; t = 8