Q8. - Algebra 1

Question

Simplify each expression. State the excluded values of the variables.

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

Step-by-Step Solution

Answer

The given expression can be simplified to $\frac{4}{x+7}$. Excluded values of the variable are  $-7$ and $7$.

Step 1. Factor.

Factor the given expression.

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

Step 2. Exclude the values.

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

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

Step 3. Zero product property.

Apply zero product property to above equation.

$$\begin{gathered} x+7=0\text{ or }x-7=0 \\ x=-7x=7 \end{gathered}$$

Therefore, $x\ne -7$ and $x\ne 7$.