# How do you solve x/(x-1)>2?

Feb 18, 2017

$1 < x < 2$ or in interval form: $\left(1 , 2\right)$

#### Explanation:

Put the inequality in $> 0$ form:

$\frac{x}{x - 1} - 2 > 0$

Find the common denominator:

$\frac{x}{x - 1} + \frac{- 2 \left(x - 1\right)}{x - 1} > 0$;

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

Combine under the same denominator:

$\frac{x - 2 x + 2}{x - 1} = \frac{- x + 2}{x - 1} > 0$

Key Points: $- x + 2 > 0$ and $x - 1 > 0$

Simplify: $- x > - 2$ and $x > 1$

When you divide by -1, the inequality changes direction:
(-x/-1) < (-2/-1); x < 2

Therefore: $1 < x < 2$ or in interval form: $\left(1 , 2\right)$