# How do you solve ( x-1) /3 - (x-1) /2 = 6?

Oct 12, 2016

$x = - 35$

#### Explanation:

First, we have to compute the common denominator.
The common denominator of the prime numbers $3$ and $2$ is their product $\textcolor{red}{6}$

$\frac{x - 1}{3} - \frac{x - 1}{2} = 6$

$\Rightarrow \frac{\textcolor{red}{2} \left(x - 1\right)}{\textcolor{red}{6}} - \frac{\textcolor{red}{3} \left(x - 1\right)}{\textcolor{red}{6}} = 6$

$\Rightarrow \frac{2 \left(x - 1\right) - 3 \left(x - 1\right)}{6} = 6$
$\Rightarrow 2 \left(x - 1\right) - 3 \left(x - 1\right) = 6 \cdot 6$ cross multiplication
$\Rightarrow 2 x - 2 - 3 x + 3 = 36$
$\Rightarrow 2 x - 3 x - 2 + 3 = 36$
$\Rightarrow - x + 1 = 36$
$\Rightarrow - x = 36 - 1$
$\Rightarrow - x = 35$
$\Rightarrow x = - 35$