# How do you solve 1/x=6/(5x)+1 and check for extraneous solutions?

Nov 5, 2016

I found: $x = - \frac{1}{5}$

#### Explanation:

We can use $5 x$ as common denominator and rearrange as:
$\frac{5}{\cancel{5 x}} = \frac{6 + 5 x}{\cancel{5 x}}$
$5 x = 5 - 6$
$5 x = - 1$
$x = - \frac{1}{5}$
which is an acceptable solution