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Simplify \(\frac{3}{2x - 1}\) + \(\frac{2 - x}{x - 2}\)

Mathematics
JAMB 1982

Simplify \(\frac{3}{2x - 1}\) + \(\frac{2 - x}{x - 2}\)
  • A. \(\frac{2 - x}{(2x - 1)(x - 2)}\)
  • B. \(\frac{5 - x}{(2x - 1)(x - 2)}\)
  • C. \(\frac{4 - 2x}{2x - 1}\)
  • D. \(\frac{6 - 3x}{(2x - 1)(x - 2)}\)
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Correct Answer: Option C
Explanation
\(\frac{3}{2x - 1}\) + \(\frac{2 - x}{x - 2}\)

= \(\frac{3}{2x - 1}\) - \(\frac{x - 2}{x - 2}\)

= \(\frac{3}{2x - 1}\) - 1

= \(\frac{3 - (2x - 1)}{2x - 1}\)

= \(\frac{3 - 2x + 1}{2x - 1}\)

= \(\frac{4 - 2x}{2x - 1}\)

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