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

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

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

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

x < 1 or x \geq 2

Interval Notation

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

Solution steps

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

Rewrite in standard form

\frac{- 2 x + 4}{x - 1} \leq 0

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Divide both sides by

2

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

Simplify

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

Identify the intervals

x < 1 or x \geq 2

5 x^{3} - 17 x^{2} + 17 x - 5 \leq 0

(x + 2)^{2} - (x - 2)^{2} > 8 x - 2

\frac{( x ^{3} + 1 )}{( 7 x ^{2} - 1 )} \leq 0

\frac{1}{( x ^{2} )} \leq 4

\frac{( 3 x - x ^{4} )}{( ( x + 4 ) ^{2} )} \geq 0