What is (x-1)/(x^2-1)<= 1 ?

The solution to (x-1)/(x^2-1) = 0

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(x-1)/(x^2-1)<= 1

\frac{x - 1}{x ^{2} - 1} \leq 1

x < - 1 or x \geq 0

Solution steps

\frac{x - 1}{x ^{2} - 1} \leq 1

Rewrite in standard form

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

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

\frac{x}{x + 1} \geq 0

Identify the intervals

x < - 1 or x \geq 0

9 (1 - 9 v) = - 477

x^{3} - 19 x - 30

4 m^{2} - 121 = 0

\frac{n}{9} < \frac{n}{2} - \frac{1}{3}

(\frac{2 i}{n})^{2}