Question

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

Answer 1

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 `color(red)(49)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`n^2 - 49 + color(red)(49) = 0 + color(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) = +-sqrt(49)`

`n = +-7`

There excluded values are:

`n = -7` and `n = 7`

Answer 2

`n !=2 and x!=-2`

Explanation:

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

`(-n)/(n^2-49)" "larr` factorise the denominator

`(-n)/((n+2)(n-2))`

Neither bracket may be equal to `0`.

`n+2 != 0 rarr n !=-2`

`n-2 != 0 rarr n!= 2`

These are the excluded values.#