How do you solve $\frac{x}{x - 1} > 2$ $x/(x-1)>2$ ?

Question

5991 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-18T02:30:59

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

Put the inequality in $> 0$ $> 0$ form:

$\frac{x}{x - 1} - 2 > 0$ $x/(x-1) -2 > 0$

Find the common denominator:

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

Remember: $- 2 (x - 1) = - 2 x + 2$ $-2(x-1) = -2x+2$

Combine under the same denominator:

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

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

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

When you divide by -1, the inequality changes direction:
$(- \frac{x}{- 1}) < (- \frac{2}{- 1}); x < 2$ $(-x/-1) < (-2/-1); x < 2$

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

How do you solve xx−1>2x/(x-1)>2?