- In this question you must show all stages of your working.
\section*{Solutions relying on calculator technology are not acceptable.}
Given that
$$\frac { x + 2 } { x + 4 } \leqslant \frac { x } { k ( x - 1 ) }$$
where \(k\) is a positive constant,
- show that
$$( x + 4 ) ( x - 1 ) \left( p x ^ { 2 } + q x + r \right) \leqslant 0$$
where \(p , q\) and \(r\) are expressions in terms of \(k\) to be determined.
- Hence, or otherwise, determine the values for \(x\) for which
$$\frac { x + 2 } { x + 4 } \leqslant \frac { x } { 3 ( x - 1 ) }$$