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

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

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

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

x > - 2

Interval Notation

(- 2, \infty)

Solution steps

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

Rewrite in standard form

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

Identify the intervals

x > - 2

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

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

\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

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