A student attempts to write 2x2−21x(x+2)(x−3)2\displaystyle \frac{2x^2 - 21x}{(x+2)(x-3)^2}(x+2)(x−3)22x2−21x in partial fractions with constant numerators.
Their incorrect attempt is shown below:
Step 1 2x2−21x(x+2)(x−3)2≡A(x+2)+B(x−3)2\displaystyle \frac{2x^2 - 21x}{(x+2)(x-3)^2} \equiv \frac{A}{(x+2)} + \frac{B}{(x-3)^2}(x+2)(x−3)22x2−21x≡(x+2)A+(x−3)2B
Step 2 2x2−21x≡A(x−3)2+B(x+2)2x^2 - 21x \equiv A(x-3)^2 + B(x+2)2x2−21x≡A(x−3)2+B(x+2)
Step 3 Let x=3⇒B=−9x = 3 \Rightarrow B = -9x=3⇒B=−9 Let x=−2⇒A=2x = -2 \Rightarrow A = 2x=−2⇒A=2
Answer 2(x+2)−9(x−3)2\displaystyle \frac{2}{(x+2)} - \frac{9}{(x-3)^2}(x+2)2−(x−3)29
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.