What is | x/(x+1)|>x ?

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

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| x/(x+1)|>x

\frac{x}{x + 1} > x

x < - 1 or - 1 < x < 0

Solution steps

\frac{x}{x + 1} > x

Find positive and negative intervals

x < - 1, - 1 \leq x < 0, x \geq 0

Solve the inequality for each interval

x < - 1 or - 1 < x < 0 or No Solution

Merge Overlapping Intervals

x < - 1 or - 1 < x < 0

\frac{1}{10} + \frac{1}{15}

\frac{x}{5} - 2 \geq 1

11 + b = - 22

12 g - 19 = 3 g - 31

\frac{x}{( x - 3 )} > \frac{( x + 1 )}{( x + 3 )}