Partial fractions — A/L Combined Mathematics

How do I practise Partial fractions?

1 question with a worked solution

1. What is the partial fraction decomposition of the rational function f(x) = (2x + 3) / [(x + 1)(x + 2)]?
   1. A) 1 / (x + 1) + 1 / (x + 2)
   2. B) 1 / (x + 1) - 1 / (x + 2)
   3. C) 2 / (x + 1) + 3 / (x + 2)
   4. D) 3 / (x + 1) - 1 / (x + 2)
   Check my answer

   Correct answer: A) 1 / (x + 1) + 1 / (x + 2)

   Let (2x + 3) / [(x + 1)(x + 2)] = A / (x + 1) + B / (x + 2). Then 2x + 3 = A(x + 2) + B(x + 1). Setting x = -1: 2(-1) + 3 = A(1) => A = 1. Setting x = -2: 2(-2) + 3 = B(-1) => -1 = -B => B = 1. Thus, f(x) = 1 / (x + 1) + 1 / (x + 2).

   Show worked solution

   Step 1: Set up: 2x + 3 = A(x + 2) + B(x + 1). Step 2: x = -1 => 1 = A(1) => A = 1. Step 3: x = -2 => -1 = B(-1) => B = 1. Answer: 1 / (x + 1) + 1 / (x + 2).
   Modelled on: the A/L Combined Mathematics examination pattern

Get this auto-marked

Next in the syllabus

Where does Partial fractions fit in the syllabus?

Year 1 · Term 1