What is ((2*(x-2)^3+9))/((x*(x+2)^2))>2 ?

The solution to ((2*(x-2)^3+9))/((x*(x+2)^2))>2 is x<-2\lor-2<x<0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

((2(x-2)^3+9))/((x(x+2)^2))>2

\frac{( 2 \cdot ( x - 2 ) ^{3} + 9 )}{( x \cdot ( x + 2 ) ^{2} )} > 2

x < - 2 or - 2 < x < 0

Interval Notation

(- \infty, - 2) \cup (- 2, 0)

Solution steps

\frac{2 ( x - 2 ) ^{3} + 9}{x ( x + 2 ) ^{2}} > 2

Rewrite in standard form

\frac{- 20 x ^{2} + 16 x - 7}{x ( x + 2 ) ^{2}} > 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( 20 x ^{2} - 16 x + 7 ) ) ( - 1 )}{x ( x + 2 ) ^{2}} < 0 \cdot (- 1)

Simplify

\frac{20 x ^{2} - 16 x + 7}{x ( x + 2 ) ^{2}} < 0

Identify the intervals

x < - 2 or - 2 < x < 0

(x - 3) 2 > (x - 7) (x + 9)

\frac{8 x}{x + 1} < 8

193 x^{2} - 7 x + 4 \leq 0

\frac{x}{( x + 4 )} - \frac{1}{( x + 1 )} \leq 0

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

What is ((2*(x-2)^3+9))/((x*(x+2)^2))>2 ?
The solution to ((2*(x-2)^3+9))/((x*(x+2)^2))>2 is x<-2\lor-2<x<0