JAMB 1985 · UME · Q11

Write $h$ in terms of $a$ , $b$ , $c$ and $d$ if $a = \dfrac{b(1 - ch)}{1 - dh}$ .

Worked solution (try it first)

Multiply both sides by $1 - dh$ and expand: $a - adh = b - bch$ .
Collect the $h$ terms on one side: $bch - adh = b - a$ , so $h(bc - ad) = b - a$ .
Divide by $bc - ad$ : $h = \frac{b - a}{bc - ad}$ .
Multiply top and bottom by $-1$ to get $h = \dfrac{a - b}{ad - bc}$ , option A.