GCEFurther MathematicsPolynomials and Partial Fractions2022

Which of the following is the correct partial fraction decomposition of $\dfrac{7}{(x-1)(x+6)}$?

A$\dfrac{1}{x - 1} - \dfrac{1}{x + 6}$CORRECT
B$\dfrac{1}{x - 1} + \dfrac{1}{x + 6}$
C$\dfrac{7}{x - 1} - \dfrac{7}{x + 6}$
D$\dfrac{-1}{x - 1} + \dfrac{1}{x + 6}$
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Why the answer is A, and why the others tempt you.
Let 7/[(x-1)(x+6)] = A/(x-1) + B/(x+6). Then 7 = A(x+6) + B(x-1). Setting x=1: 7 = 7A, so A=1. Setting x=-6: 7 = -7B, so B=-1. The decomposition is 1/(x-1) - 1/(x+6).
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