What is x/(x+2)<= 1/x ?

The solution to x/(x+2)<= 1/x is -2<x<=-1\lor 0<x<= 2

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x/(x+2)<= 1/x

\frac{x}{x + 2} \leq \frac{1}{x}

- 2 < x \leq - 1 or 0 < x \leq 2

Solution steps

\frac{x}{x + 2} \leq \frac{1}{x}

Rewrite in standard form

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

Factor

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

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

Identify the intervals

- 2 < x \leq - 1 or 0 < x \leq 2

6^{- 6}

4 (2 - x) < - 6 and \frac{x - 1}{4} \leq - 1

(9 f - 4) (- 8 f + 7) = 0

10 a^{2} b^{3} c^{4} - 15 a^{4} b^{2} c^{4} + 30 a^{4} b^{3} c^{2}

4 x - 8 \geq 12