# Question #8d374

Aug 22, 2017

See a solution process below:

#### Explanation:

Because we are not allowed to divide by $0$ the excluded values for the expression: $\frac{5 x + 15}{{x}^{2} - 49}$ are ${x}^{2} - 49 \ne 0$

To find the values of $x$ where this exclusion is true we need to solve the denominator for $0$:

${x}^{2} - 49 = 0$

${x}^{2} - 49 + \textcolor{red}{49} = 0 + \textcolor{red}{49}$

${x}^{2} - 0 = 49$

${x}^{2} = 49$

$\sqrt{{x}^{2}} = \pm \sqrt{49}$

$x = \pm 7$

The excluded values are: $x \ne - 7$ and $x \ne 7$