Discussion
The partial fraction decomposition of \( \dfrac{1}{(x-1)(x-2)} \) is
Answer: A
Write \( 1 = A(x-2) + B(x-1) \). Setting \( x = 1 \) gives \( A = -1 \), and setting \( x = 2 \) gives \( B = 1 \), so
\[ \frac{1}{(x-1)(x-2)} \;=\; \frac{-1}{x-1} + \frac{1}{x-2}. \]
A quick check at \( x = 0 \) gives \( 1/2 \) on both sides, so the signs are the right way round
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