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

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

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

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

- 1 < x < 1 or x \geq 2

Interval Notation

(- 1, 1) \cup [2, \infty)

Solution steps

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

Rewrite in standard form

\frac{2 x - 4}{( x + 1 ) ( x - 1 )} \geq 0

Factor

\frac{2 x - 4}{( x + 1 ) ( x - 1 )} : \frac{2 ( x - 2 )}{( x + 1 ) ( x - 1 )}

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

Divide both sides by

2

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

Simplify

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

Identify the intervals

- 1 < x < 1 or x \geq 2

\frac{k}{6} = \frac{15}{18}

x^{2} - x = \frac{2}{9} - \frac{2 x}{3}

\frac{6 x + 1}{12} - \frac{x - 13}{9} = \frac{5 x - 3}{2} + \frac{x}{30}

12 z^{2} + 1 z - 1 = 0

9 \cdot \frac{4}{3}

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