# How do you solve 1/(n-8)-1=7/(n-8) and check for extraneous solutions?

Jul 12, 2017

#### Answer:

$n = 2$

#### Explanation:

$\frac{1}{n - 8} - 1 = \frac{7}{n - 8}$

Subtracting $\frac{1}{n - 8}$ from both sides,

$- 1 = \frac{6}{n - 8}$

$8 - n = 6$

$n = 2$

This solution works, as we notice that $n = 8$ is the only extraneous value, but is not an actual solution (as it makes the denominator 0).