What is (2+3)/((x+1))>= 2/x ?

The solution to (2+3)/((x+1))>= 2/x is -1 = 2/3

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(2+3)/((x+1))>= 2/x

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

- 1 < x < 0 or x \geq \frac{2}{3}

Interval Notation

(- 1, 0) \cup [\frac{2}{3}, \infty)

Decimal Notation

- 1 < x < 0 or x \geq 0.66666 \dots

Solution steps

\frac{2 + 3}{x + 1} \geq \frac{2}{x}

Rewrite in standard form

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

Identify the intervals

- 1 < x < 0 or x \geq \frac{2}{3}

\frac{( x + 3 )}{( 5 x )} > 0

3 x + \frac{8}{x} - 1 < - \frac{2}{1}

\frac{( - x + 5 )}{( x - 2 )} < 0

\frac{3}{( x - 2 )} < 0

\frac{( [ x ] - 6 )}{( 8 - [ x ] )} > 0

What is (2+3)/((x+1))>= 2/x ?
The solution to (2+3)/((x+1))>= 2/x is -1<x<0\lor x>= 2/3