What is |((x-1))/((2-x))|>0 ?

The solution to |((x-1))/((2-x))|>0 is x 2

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

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

x < 1 or 1 < x < 2 or x > 2

Interval Notation

(- \infty, 1) \cup (1, 2) \cup (2, \infty)

Solution steps

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

Apply absolute rule: If

∣ u ∣ > 0

then

u < 0

u > 0

\frac{x - 1}{2 - x} < 0 or \frac{x - 1}{2 - x} > 0

\frac{x - 1}{2 - x} < 0 or \frac{x - 1}{2 - x} > 0

(x < 1 or x > 2) or 1 < x < 2

Merge Overlapping Intervals

x < 1 or 1 < x < 2 or x > 2

x^{2} + 3 x + x^{2} - 2 > 0

∣ x - 4 ∣ > ∣ 2 x - 3 ∣

2^{4} x^{2} - 1 - 5 \geq 3

∣ 3 - 4353 x - 2.5 ∣ \geq 2

\frac{n}{2 - 4} > 3

What is |((x-1))/((2-x))|>0 ?
The solution to |((x-1))/((2-x))|>0 is x<1\lor 1<x<2\lor x>2