JAMB 1993 · UME · Q11

Make $x$ the subject of the relation $\dfrac{1 + ax}{1 - ax} = \dfrac pq$ .

Worked solution (try it first)

Cross-multiply: $q(1 + ax) = p(1 - ax)$ , so $q + aqx = p - apx$ .
Collect the $x$ terms on the left: $apx + aqx = p - q$ , so $ax(p + q) = p - q$ .
Divide by $a(p + q)$ : $x = \dfrac{p - q}{a(p + q)}$ , option B.