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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x < - 1 or 1 < x < 3

Interval Notation

(- \infty, - 1) \cup (1, 3)

Solution steps

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

Rewrite in standard form

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

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x + 1 ) ( x - 3 ) ) ( - 1 )}{x - 1} < 0 \cdot (- 1)

Simplify

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

Identify the intervals

x < - 1 or 1 < x < 3

\frac{x ^{2}}{x - 1} \geq 0

\frac{( x - 9 ) ( x - 15 )}{( x - 12 )} > 0

m^{2} + 8 > 0

5 (x - 2) (x + 2) < 12

\frac{( x - 11 )}{( x - 12 )} < 0