Simplify the rational expression. State any restrictions on the variable. t²- 4t - 32/ t - 8

Solution:

The ratio expression given in the problem can be simplified as shown below:

t²- 4t - 32/ t - 8, t ≠ 8

The numerator t² - 4t - 32 can be factorized as

t²- 8t + 4t - 32 (using the factors 4 and 8 of 32)

t(t - 8) + 4(t - 8)

(t - 8)(t + 4)

Therefore,

t²- 4t - 32/ t - 8 = (t - 8)(t + 4)/(t - 8)

Since t ≠ 8 we get

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

Simplify the rational expression. State any restrictions on the variable. t²- 4t - 32/ t - 8

Summary:

The rational expression t²- 4t - 32/ t - 8 can be simplified as t + 4 with the restriction on the variable t that t ≠ 8.