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

The solution to |(x-1)/(x-2)|>x is x<(3-sqrt(5))/2 \lor (1+sqrt(5))/2 <x<2\lor 2<x<(3+sqrt(5))/2

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

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

x < \frac{3 - 5}{2} or \frac{1 + 5}{2} < x < 2 or 2 < x < \frac{3 + 5}{2}

Interval Notation

(- \infty, \frac{3 - 5}{2}) \cup (\frac{1 + 5}{2}, 2) \cup (2, \frac{3 + 5}{2})

Decimal Notation

x < 0.38196 \dots or 1.61803 \dots < x < 2 or 2 < x < 2.61803 \dots

Solution steps

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

Find positive and negative intervals

x \leq 1, 1 < x < 2, x \geq 2

Solve the inequality for each interval

x < \frac{3 - 5}{2} or \frac{1 + 5}{2} < x < 2 or 2 < x < \frac{3 + 5}{2}

27 - 12 x^{2}

3 x + 6 = 0

1530 = \frac{1}{2} \cdot 0.55 \cdot (58.3749 6^{2} + x^{2})

8 x (x + 2) = 0

x^{2} - 12 x + 22 = 0

What is |(x-1)/(x-2)|>x ?
The solution to |(x-1)/(x-2)|>x is x<(3-sqrt(5))/2 \lor (1+sqrt(5))/2 <x<2\lor 2<x<(3+sqrt(5))/2