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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

Respuesta :

Nirina7
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
boffeemadrid

Answer:

(C)t+4; t=8

Step-by-step explanation:

The given rational expression is:

[tex]\frac{t^2-4t-32}{t-8}[/tex]

Simplifying the above expression, we get

=[tex]\frac{t^2-8t+4t-32}{t-8}[/tex]

=[tex]\frac{t(t-8)+4(t-8)}{t-8}[/tex]

=[tex]\frac{(t+4)(t-8)}{(t-8)}[/tex]

=[tex]t+4[/tex]

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.

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