# How do you solve 2+ \frac { 1} { x } = 3+ \frac { 2} { x }?

Apr 20, 2018

$x = - 1$

#### Explanation:

Identify like terms
$2 + \setminus \textcolor{red}{\frac{1}{x}} = 3 + \setminus \textcolor{red}{\frac{2}{x}}$

Put all non-variable stuff on left side
$2 - 3 + \setminus \textcolor{red}{\frac{1}{x}} = \setminus \textcolor{red}{\frac{2}{x}}$

Put all variable stuff on right side
$2 - 3 = \setminus \textcolor{red}{\frac{2}{x} - \frac{1}{x}}$

Simplify both sides
$- 1 = \setminus \textcolor{red}{\frac{1}{x}}$

$- 1 = \frac{1}{x}$ means $1 = - 1 \cdot x$, thus $x = \frac{1}{-} 1$
Then $x = - 1$.