JAMB 1994 · UME · Q14

Linear & simultaneous equations

If $a = 1$ and $b = 3$ , solve for $x$ in the equation $\dfrac{a}{a - x} = \dfrac{b}{x - b}$ .

Worked solution (try it first)

Put in $a = 1$ and $b = 3$ : $\dfrac{1}{1 - x} = \dfrac{3}{x - 3}$ .
Cross-multiply: $x - 3 = 3(1 - x)$ , so $x - 3 = 3 - 3x$ .
Add $3x$ and 3 to both sides: $4x = 6$ .
Divide by 4: $x = \frac32$ , option C.

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