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

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Answer 1 · 2017-02-18T02:30:59

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

Put the inequality in $> 0$ form:

$x/(x-1) -2 > 0$

Find the common denominator:

$x/(x-1) + (-2(x-1))/(x-1) > 0$ ;

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

Combine under the same denominator:

$(x -2x+2)/(x-1) = (-x+2)/(x-1) > 0$

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: $(1, 2)$

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