Word Count : 310

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We are asked to express $$ \frac{x-1}{x^3 - x^2 - 2x} $$ as a sum of partial fractions. First, factor the denominator: $$ x^3 - x^2 - 2x = x(x^2 - x - 2) = x(x-2)(x+1) $$ So we can write: $$ \frac{x-1}{x(x-2)(x+1)} = \frac{A}{x} + \frac{B}{x-2} + \frac{C}{x+1} $$ Multiply both sides by $x(x-2)(x+1)$: $$ x-1 = A(x-2)(x+1) + B x(x+1) ____ _____ ___ __________ __________ _________ __________ _______ __________.
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