What is (x/(-(x+2)))/x*(x-2)<0 ?

The solution to (x/(-(x+2)))/x*(x-2) 2

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(x/(-(x+2)))/x*(x-2)<0

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

x < - 2 or x > 2

Interval Notation

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

Solution steps

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

Rewrite in standard form

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

Identify the intervals

x < - 2 or x > 2

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

\frac{( x - 3 ) ( x - 4 )}{( 2 x ^{2} - 4 x + 5 )} > 0

(x^{2} - 2 x) (3 x - 6) \leq 0

\frac{( x - 1 )}{( x - 2 )} + \frac{( x + 1 )}{( 3 - x )} \leq 1

9 x^{2} - 20 x + 11 > 0

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