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

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

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x/((x-1))>((x-1))/x

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

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

Interval Notation

(0, \frac{1}{2}) \cup (1, \infty)

Decimal Notation

0 < x < 0.5 or x > 1

Solution steps

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

Rewrite in standard form

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

Identify the intervals

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

\frac{20 ( x - 2 )}{( x ^{2} + 1 )} < \frac{- 1}{2}

x^{2} (x - 2) (x - 3) (1 - x) (1 + x) \geq 0

\frac{1}{( x ^{2} - 5 x + 6 )} \geq \frac{1}{2}

(x - 1) (x^{2} - 2 x + 1) > 0

3 x^{2} - 27 > 0

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