1. A student was set the following problem.

Use algebra to find the set of values of \(x\) for which $$\frac { x } { x - 24 } > \frac { 1 } { x + 11 }$$ The student's attempt at a solution is written below. $$\begin{gathered} x ( x - 24 ) ( x + 11 ) ^ { 2 } > ( x + 11 ) ( x - 24 ) ^ { 2 }
x ( x - 24 ) ( x + 11 ) ^ { 2 } - ( x + 11 ) ( x - 24 ) ^ { 2 } > 0
( x - 24 ) ( x + 11 ) [ x ( x + 11 ) - x - 24 ] > 0
( x - 24 ) ( x + 11 ) \left[ x ^ { 2 } + 10 x - 24 \right] > 0
( x - 24 ) ( x + 11 ) ( x + 12 ) ( x - 2 ) > 0
x = 24 , x = - 11 , x = - 12 , x = 2
\{ x \in \mathbb { R } : - 12 < x < - 11 \} \cup \{ x \in \mathbb { R } : 2 < x < 24 \} \end{gathered}$$ Line 3 There are errors in the student's solution.

1. Identify the error made
   1. in line 3
   2. in line 7
2. Find a correct solution to this problem.