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

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

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

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

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

Interval Notation

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

Decimal Notation

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

Solution steps

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

Rewrite in standard form

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

Identify the intervals

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

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

(x - 3) (x - 1) > 15

\frac{x}{5 - 5} > 2

\frac{( x - 1 )}{( 4 x + 5 )} < \frac{( x - 3 )}{( 4 x - 3 )}

(x - 3) (x + 1) < 0

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