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

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

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

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

- 1 < n < 0 or 0 < n < 1

Interval Notation

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

Solution steps

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

Rewrite in standard form

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

Factor

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

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

Identify the intervals

- 1 < n < 0 or 0 < n < 1

\frac{( ( x + 1 ) ^{2} \cdot ( x - 5 ) ^{3} )}{( ( x - 4 ) ( x + 2 ) )} \geq 0

(x - 3) (x + 7) > 0

x^{2} + 3 < 0

- 10 x^{4} + 70 x^{3} - 60 x^{2} > 0

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

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