# How do you multiply 3 /(x - 1) + 1 / (x(x - 1)) = 2 / x?

Jun 5, 2018

Assuming the question really was "solve for "$x$:
$\textcolor{w h i t e}{\text{XXX}} x = - 3$

#### Explanation:

1 Multiply both sides by the Least Common Denominator [namely $x \left(x - 1\right)$]
$\textcolor{w h i t e}{\text{XXX}} 3 x + 1 = 2 \left(x - 1\right)$

2 Simplify
$\textcolor{w h i t e}{\text{XXX}} 3 x + 1 = 2 x - 2$

3 Subtract $2 x$ from both sides
$\textcolor{w h i t e}{\text{XXX}} 3 x + 1 - 2 x = - 2$

4 Simplify $3 x + 1 - 2 x$ to $x + 1$
$\textcolor{w h i t e}{\text{XXX}} x + 1 = - 2$

5 Subtract $1$ from both sides
$\textcolor{w h i t e}{\text{XXX}} x = - 2 - 1$

6 Simplify
$\textcolor{w h i t e}{\text{XXX}} x = - 3$

Jun 5, 2018

$x = - 3$

#### Explanation:

Multiply the first fraction by $x$

$\frac{3 x + 1}{x \left(x - 1\right)} = \frac{2}{x}$

Now multiply both sides by $x \left(x - 1\right)$ to remove the fractions

$3 x + 1 = 2 \left(x - 1\right)$

$3 x + 1 = 2 x - 2$

subtract $2 x$ from both sides

$x + 1 = - 2$

subtract 1 from both sides