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$\frac{x^2 + x + 1}{x^2 + x -2} \textless 0$

$\frac{(x+0.5)^2 + 0.75}{(x-1)(x+2)} \textless 0$

Since $(x+0.5)^2 + 0.75$ is always positive for all x,

$(x-1)(x+2) \textless 0$

$\therefore, - 2 \textless x \textless 1$

A very straightforward inequality question.

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