AM-154

Partial fractions

A Math · Secondary 3 · Hard · Partial fractions

Express

\dfrac{3x^3-5x^2+4}{x^3-x}

as the sum of an integer and three partial fractions of the form

\dfrac{A}{x}+\dfrac{B}{x-1}+\dfrac{C}{x+1}

.

$3+\dfrac{4}{x}-\dfrac{3}{x-1}-\dfrac{3}{x+1}$
$3+\dfrac{4}{x}+\dfrac{3}{x-1}-\dfrac{3}{x+1}$
$3+\dfrac{4}{x}-\dfrac{3}{x-1}+\dfrac{3}{x+1}$
$3-\dfrac{4}{x}-\dfrac{3}{x-1}-\dfrac{3}{x+1}$

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