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JAMB Mathematics 1995 Question 19

Question 19

Polynomials

Express (5x − 12)/((x − 2)(x − 3)) in partial fractions.

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

Answer: B (2/(x − 2) + 3/(x − 3))

Explanation

Write 5x − 12 = A(x − 3) + B(x − 2). x = 2 gives −2 = −A, so A = 2; x = 3 gives 3 = B. So it is 2/(x − 2) + 3/(x − 3).