What is -(2(-3x^2-1))/((x^2-1)^3)>0 ?

The solution to -(2(-3x^2-1))/((x^2-1)^3)>0 is x 1

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-(2(-3x^2-1))/((x^2-1)^3)>0

- \frac{2 ( - 3 x ^{2} - 1 )}{( x ^{2} - 1 ) ^{3}} > 0

x < - 1 or x > 1

Interval Notation

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

Solution steps

- \frac{2 ( - 3 x ^{2} - 1 )}{( x ^{2} - 1 ) ^{3}} > 0

Rewrite in standard form

\frac{- 3 x ^{2} - 1}{( x ^{2} - 1 ) ^{3}} < 0

Factor

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

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

Identify the intervals

x < - 1 or x > 1

2 x^{3} - 5 x

1 = 2 x^{2} - x

(x^{- 4})^{3}

\frac{3 ^{2}}{- 4}

0 = 48 t - 16 t^{2}

What is -(2(-3x^2-1))/((x^2-1)^3)>0 ?
The solution to -(2(-3x^2-1))/((x^2-1)^3)>0 is x<-1\lor x>1