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

The solution to ((x^2+2))/((x^2-1))<-2 is -1<x<0\lor 0<x<1

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

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

- 1 < x < 0 or 0 < x < 1

Interval Notation

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

Solution steps

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

Rewrite in standard form

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

Factor

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

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

Identify the intervals

- 1 < x < 0 or 0 < x < 1

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

\frac{1}{( x + 2 )} < \frac{3}{( x - 3 )}

\frac{0.5}{( x - x ^{2} - 1 )} < 0

x^{3} - 7 x^{2} + 14 x - 8 < 0

\frac{x}{( x - 2 )} > \frac{1}{( x + 3 )}

What is ((x^2+2))/((x^2-1))<-2 ?
The solution to ((x^2+2))/((x^2-1))<-2 is -1<x<0\lor 0<x<1