What is (4(x^2+2))/((x^2-1))<-2 ?

The solution to (4(x^2+2))/((x^2-1))<-2 is -1<x<1

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

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

- 1 < x < 1

Interval Notation

(- 1, 1)

Solution steps

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

Rewrite in standard form

\frac{6 x ^{2} + 6}{x ^{2} - 1} < 0

Factor

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

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

Divide both sides by

6

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

Simplify

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

Identify the intervals

- 1 < x < 1

(x - 5)^{3} + 9 \geq 10

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

\frac{( 3 x + 4 )}{( 2 x - 1 )} < 2

4 x^{3} - 17 x^{2} + 21 x - 8 \geq 0

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

What is (4(x^2+2))/((x^2-1))<-2 ?
The solution to (4(x^2+2))/((x^2-1))<-2 is -1<x<1