A student attempts to write 2x2−43x(x+3)(x−4)2\displaystyle \frac{2x^2 - 43x}{(x+3)(x-4)^2}(x+3)(x−4)22x2−43x in partial fractions with constant numerators.
Their incorrect attempt is shown below:
Step 1 2x2−43x(x+3)(x−4)2≡A(x+3)+B(x−4)2\displaystyle \frac{2x^2 - 43x}{(x+3)(x-4)^2} \equiv \frac{A}{(x+3)} + \frac{B}{(x-4)^2}(x+3)(x−4)22x2−43x≡(x+3)A+(x−4)2B
Step 2 2x2−43x≡A(x−4)2+B(x+3)2x^2 - 43x \equiv A(x-4)^2 + B(x+3)2x2−43x≡A(x−4)2+B(x+3)
Step 3 Let x=4⇒B=−20x = 4 \Rightarrow B = -20x=4⇒B=−20 Let x=−3⇒A=3x = -3 \Rightarrow A = 3x=−3⇒A=3
Answer 3(x+3)−20(x−4)2\displaystyle \frac{3}{(x+3)} - \frac{20}{(x-4)^2}(x+3)3−(x−4)220
Explain the mistake that the student has made in step 1.
368 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.