What is ((2(x-3)))/((x(x-6)))-1/((x-1))<= 0 ?

The solution to ((2(x-3)))/((x(x-6)))-1/((x-1))<= 0 is x<0\lor 1<x<6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

((2(x-3)))/((x(x-6)))-1/((x-1))<= 0

\frac{( 2 ( x - 3 ) )}{( x ( x - 6 ) )} - \frac{1}{( x - 1 )} \leq 0

x < 0 or 1 < x < 6

Interval Notation

(- \infty, 0) \cup (1, 6)

Solution steps

\frac{2 ( x - 3 )}{x ( x - 6 )} - \frac{1}{x - 1} \leq 0

Rewrite in standard form

\frac{x ^{2} - 2 x + 6}{x ( x - 6 ) ( x - 1 )} \leq 0

Identify the intervals

x < 0 or 1 < x < 6

\frac{x - 2}{x ^{2} + 1} < 0

\frac{2}{x - 1} < 1

(x + 2) (x - 1) (x + 4) < 0

(x^{2} - 64) \cdot (x^{2} - 36) < 0

x^{2} > - 6 - 5 x

What is ((2(x-3)))/((x(x-6)))-1/((x-1))<= 0 ?
The solution to ((2(x-3)))/((x(x-6)))-1/((x-1))<= 0 is x<0\lor 1<x<6