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 \(\frac{3}{4}\)
jamb 1994mathematics

The correct answer is C. \(\frac{3}{2}\)

Let's solve the equation \(\frac{a}{a - x}\) = \(\frac{b}{x - b}\) for x, given that a = 1 and b = 3.

Substituting these values into the equation, we get \(\frac{1}{1 - x}\) = \(\frac{3}{x - 3}\). Cross-multiplying, we get \(x - 3 = 3(1 - x)\), which simplifies to \(x - 3 = 3 - 3x\). 

Solving for x, we find that \(4x = 6\), so \(x = \frac{6}{4} = \frac{3}{2}\). 

So, the solution to the equation is x = \(\frac{3}{2}\).

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