What is (3x-5)/(x-2)>= 4/(x+1) ?

The solution to (3x-5)/(x-2)>= 4/(x+1) is x 2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(3x-5)/(x-2)>= 4/(x+1)

\frac{3 x - 5}{x - 2} \geq \frac{4}{x + 1}

x < - 1 or x = 1 or x > 2

Interval Notation

(- \infty, - 1) \cup x = 1 \cup (2, \infty)

Solution steps

\frac{3 x - 5}{x - 2} \geq \frac{4}{x + 1}

Rewrite in standard form

\frac{3 x ^{2} - 6 x + 3}{( x - 2 ) ( x + 1 )} \geq 0

Factor

\frac{3 x ^{2} - 6 x + 3}{( x - 2 ) ( x + 1 )} : \frac{3 ( x - 1 ) ^{2}}{( x - 2 ) ( x + 1 )}

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

Divide both sides by

3

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

Simplify

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

Identify the intervals

x < - 1 or x = 1 or x > 2

2 x^{2} - 2 x

3 (x + 3)^{2} = 0

\frac{x}{2} + \frac{3}{2} = \frac{x + 3}{6}

- x^{2} + 6 x - 30 = 0

\frac{2 π}{( \frac{π}{3} )}

What is (3x-5)/(x-2)>= 4/(x+1) ?
The solution to (3x-5)/(x-2)>= 4/(x+1) is x<-1\lor x=1\lor x>2