Chapter 11, Problem 8PT

To determine

To simplify: the expression and state the Excluded value of the variables.

Answer to Problem 8PT

The simplified expression is $\frac{4}{x+7}$ and the excluded value is $-7,7$ .

Explanation of Solution

Given: $\frac{4x-28}{x^2-49}$

Calculation:

The objectives is to simplify the expression and state the excluded value of the variables.

The rational expression is simplified below.

  $\begin{array}{l}\frac{4x-28}{x^2-49}\\ =\frac{4\left(x-7\right)}{\left(x-7\right)\left(x+7\right)}\\ =\frac{4}{x+7}\end{array}$

Therefore, the simplified expression is $\frac{4}{x+7}$ .

Exclude the values for which $x^2-49=0$ .

So,

  $\begin{array}{l}{x}^2-49=0\\ \left(x-7\right)\left(x+7\right)=0\\ x=-7,7\end{array}$

Therefore, the excluded value is $-7,7$ .

Conclusion:

Therefore, the simplified expression is $\frac{4}{x+7}$ and the excluded value is $-7,7$ .