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

Oct 16, 2016

$x = - 35$

#### Explanation:

Start by making sure that you're working with fractions that have equal denominators.

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

The common denominator here is $6$, so multiply the first fraction by $1 = \frac{2}{2}$, the second fraction by $1 = \frac{3}{3}$, and the third fraction by $1 = \frac{6}{6}$.

This will get you

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

$\frac{2 \left(x - 1\right)}{6} - \frac{3 \left(x - 1\right)}{6} = \frac{36}{6}$

At this point, drop the denominators and focus exclusively on the numerators.

$2 \left(x - 1\right) - 3 \left(x - 1\right) = 36$

This will get you

$- \left(x - 1\right) = 36$

$- x + 1 = 36$

$x = - 35$

Do a quick check to make sure that the calculations are correct

$\frac{- 35 - 1}{3} - \frac{- 35 - 1}{2} = 6$

$- \frac{36}{3} + \frac{36}{2} = 6$

$- 12 + 18 = 6 \text{ } \textcolor{g r e e n}{\sqrt{}}$