2.
\includegraphics[max width=\textwidth, alt={}, center]{d6befd60-de40-41b6-8ae5-48656dbca40c-1_734_1228_888_479}
The diagram above shows a sketch of the curve with equation
$$y = \frac { x ^ { 2 } - 1 } { | x + 2 | } , \quad x \neq - 2$$
The curve crosses the \(x\)-axis at \(x = 1\) and \(x = - 1\) and the line \(x = - 2\) is an asymptote of the curve.
- Use algebra to solve the equation \(\frac { x ^ { 2 } - 1 } { | x + 2 | } = 3 ( 1 - x )\).
- Hence, or otherwise, find the set of values of \(x\) for which
$$\frac { x ^ { 2 } - 1 } { | x + 2 | } < 3 ( 1 - x )$$
(Total 9 marks)