# Given the equation x/y+5x=6+1/y, where x can be any real number except 1 or 6/5. If y is solved in terms of x, the result is y=?

Nov 8, 2017

$y = \frac{x - 1}{6 - 5 x}$

#### Explanation:

You can rearrange the equation as:

$\frac{x}{y} - \frac{1}{y} = 6 - 5 x$

Factoring out $\frac{1}{y}$ in the left hand side,
$\frac{1}{y} \left(x - 1\right) = 6 - 5 x$

Dividing both sides by $\left(x - 1\right)$,
$\frac{1}{y} = \frac{6 - 5 x}{x - 1}$

Taking the reciprocal of both sides,
$y = \frac{x - 1}{6 - 5 x}$