Question

Simplify the rational expression. State any restrictions on the variable. t^2-4t-32/t-8

Answer 1

Answer:

The simplest form of  $\frac{t^2-4t-32}{t-8}$ is t+4.

Step-by-step explanation:

We are given an expression $\frac{t^2-4t-32}{t-8}$.

Factorizing the numerator such that the factors when multiplied give a product of -32 and when added give a result of -4:

$\frac{t^2-4t-32}{t-8}$

$=\frac{t^2-8t+4t-32}{t-8}$

$= \frac{t(t-8)+4(t-8)}{t-8}$

$=\frac{(t+4)(t-8)}{t-8}$

$= t+4$

Since the denominator is $t-8$ in this expression, therefore $t\neq 8$ or it will be equal to zero which will make the overall value of the fraction undefined.

Answer 2

1. Factor the expression $t^2-4t-32:$

$t^2-4t-32=(t-8)(t+4).$

2. Since $t-8$ is placed in the denominator of the given expression, then $t\neq 8.$

3. Now the expression can be simplified:

$\dfrac{t^2-4t-32}{t-8}=\dfrac{(t-8)(t+4)}{t-8}=t+4.$