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UI Post-UTME Mathematics 2014 Question 20

Question 20

Polynomials

Find the pair (A, B) such that (x + 3)/(4x2 − 9) = A/(2x + 3) + B/(2x − 3)

  1. A.(−1/4, 3/4)
  2. B.(−3/4, 1/4)
  3. C.(3/4, −1/4)
  4. D.(1/4, 3/4)
Show the answer and explanation

Answer: A ((−1/4, 3/4))

Explanation

A(2x − 3) + B(2x + 3) = x + 3. At x = 3/2, 6B = 9/2 so B = 3/4; at x = −3/2, −6A = 3/2 so A = −1/4.