# 2011 H2 Mathematics Paper 1 Question 1

Equations and Inequalities

${- 2 < x < 1}$
\begin{align*} \frac{x^2 + x + 1}{x^2 + x - 2} &< 0 \\ \frac{\left(x + \frac{1}{2}\right)^2 + \frac{3}{4}}{(x + 2)(x - 1)} &< 0 \end{align*}
Since ${\left(x + \frac{1}{2}\right)^2 \geq 0 \; \forall x \in \mathbb{R}, }$ ${\left(x + \frac{1}{2}\right)^2 + \frac{3}{4}}$ is always positive
$\frac{1}{(x + 2)(x - 1)} < 0$
$- 2 < x < 1 \; \blacksquare$