What is (x+1}{1-x}+\frac{x-1)/x <2 ?

The solution to (x+1}{1-x}+\frac{x-1)/x 1

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

\frac{x + 1}{1 - x} + \frac{x - 1}{x} < 2

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

Interval Notation

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

Decimal Notation

x < - 1 or 0 < x < 0.5 or x > 1

Solution steps

\frac{x + 1}{1 - x} + \frac{x - 1}{x} < 2

Rewrite in standard form

\frac{2 x ^{2} + x - 1}{x ( - x + 1 )} < 0

Factor

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

\frac{( 2 x - 1 ) ( x + 1 )}{x ( - x + 1 )} < 0

Identify the intervals

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

2 x + \frac{5}{3} > \frac{2}{5} x - 1

64 - - 289

5 x + 1 = 3 x - 4

x^{2} + 4 x + 3 \leq 0

\frac{25 x ^{2} y ^{5}}{75 x y ^{3}}

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