Express $\dfrac{5x - 1}{(x+1)(x-2)}$ in partial fractions.
A$\dfrac{2}{x+1} + \dfrac{3}{x-2}$CORRECT
B$\dfrac{3}{x+1} + \dfrac{2}{x-2}$
C$\dfrac{2}{x+1} - \dfrac{3}{x-2}$
D$\dfrac{-2}{x+1} + \dfrac{3}{x-2}$
GCEFurther MathematicsPolynomials and Partial Fractions2022
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Why the answer is A, and why the others tempt you.
Let (5x-1)/[(x+1)(x-2)] = A/(x+1) + B/(x-2). Multiplying through: 5x - 1 = A(x-2) + B(x+1). Setting x = 2: 9 = 3B, so B = 3. Setting x = -1: -6 = -3A, so A = 2. The partial fractions are 2/(x+1) + 3/(x-2).
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