Express $\dfrac{5x + 1}{(x - 1)(x + 2)}$ in partial fractions.
A$\dfrac{3}{x-1} + \dfrac{2}{x+2}$
B$\dfrac{2}{x-1} - \dfrac{3}{x+2}$
C$\dfrac{2}{x-1} + \dfrac{3}{x+2}$CORRECT
D$\dfrac{5}{x-1} + \dfrac{1}{x+2}$
JUPEBMathematicsAlgebra and Surds
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Why the answer is C, and why the others tempt you.
Write $\dfrac{5x+1}{(x-1)(x+2)} = \dfrac{A}{x-1} + \dfrac{B}{x+2}$, so $5x + 1 = A(x+2) + B(x-1)$. Putting $x = 1$: $6 = 3A$, so $A = 2$. Putting $x = -2$: $-9 = -3B$, so $B = 3$. Swapping the two constants is the usual slip.
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