# What are the excluded values for (-n)/(n^2-49)?

Jul 5, 2017

See a solution process below:

#### Explanation:

The excluded values for this problem are for when the denominator is equal to $0$. We cannot divide by $0$.

Therefore, to find the excluded values we need to equate the denominator to $0$ and solve for $n$:

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

First, add $\textcolor{red}{49}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

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

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

${n}^{2} = 49$

Next, take the square root of each side of the equation to solve for $n$ while keeping the equation balanced. Remember, taking the square root of a number produces a positive and negative result:

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

$n = \pm 7$

There excluded values are:

$n = - 7$ and $n = 7$

Jul 5, 2017

$n \ne 2 \mathmr{and} x \ne - 2$

#### Explanation:

Excluded values in this case are those which will make the denominator equal to $0$. Division by zero is undefined.

$\frac{- n}{{n}^{2} - 49} \text{ } \leftarrow$ factorise the denominator

$\frac{- n}{\left(n + 2\right) \left(n - 2\right)}$

Neither bracket may be equal to $0$.

$n + 2 \ne 0 \rightarrow n \ne - 2$

$n - 2 \ne 0 \rightarrow n \ne 2$

These are the excluded values.#