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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

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

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

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

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