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If a 1 b 3 solve for x in the equation frac a a... - JAMB Mathematics 1994 Question

If a = 1, b = 3, solve for x in the equation (\frac{a}{a - x}) = (\frac{b}{x - b})

A
\(\frac{4}{3}\)
B
\(\frac{2}{3}\)
C
\(\frac{3}{2}\)
D
\(\frac{3}{4}\)
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Correct Option: C

(\frac{a}{a - x}) = (\frac{b}{x - b})

(\frac{1}{1 - x}) = (\frac{3}{x - 3})

∴ 3(1 - x) = x - 3

3 - 3x = x - 3

Rearrange 6 = 4x; x = (\frac {6}{4})

= (\frac{3}{2})

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