JAMB 2001 · UME · Q6

Expressions, formulae & change of subject

If $\frac y2 = x$ , evaluate $\dfrac{\frac{x^3}{y^3} + \frac12}{\frac12 - \frac{x^2}{y^2}}$ .

Worked solution (try it first)

From $\frac y2 = x$ , $y = 2x$ , so $\frac xy = \frac12$ .
Top: $\left(\frac12\right)^3 + \frac12 = \frac18 + \frac12$
$= \frac58$ .
Bottom: $\frac12 - \left(\frac12\right)^2 = \frac14$ .
Divide: $\frac58 \div \frac14 = \frac58 \times 4$
$= \frac52$ , option D.

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