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JAMB Mathematics 1984 Question 30

Question 30

Algebraic Expressions

If a = 2x/(1 − x) and b = (1 + x)/(1 − x) then a2 − b2 in the simplest form is

  1. A.(3x + 1)/(x − 1)
  2. B.(3x2 + 1)/(x(x − 1)2)
  3. C.(3x2 + 1)/(1 − x)2
  4. D.(5x2 − 1)/(1 − x)2
  5. E.(5x2 − 2x − 1)/(1 − x)2
Show the answer and explanation

Answer: A ((3x + 1)/(x − 1))

Explanation

a² − b² = (4x² − (1 + x)²)/(1 − x)² = (3x² − 2x − 1)/(1 − x)² = (3x + 1)(x − 1)/(x − 1)² = (3x + 1)/(x − 1).