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Partial Fractions Cheat Sheet

Linear Factors

$${\frac{cx + d}{(x - a)(x - b)(x - c)} = \frac{A}{x - a} + \frac{B}{x - b} + \frac{C}{x - c}}$$

Quadratic Factors

$${\frac{dx + f}{(x - a)(x^2 + bx + c)} = \frac{A}{x - a} + \frac{Bx + C}{x^2 + bx + c}}$$

Repeat Factors

$${\frac{cx + d}{(x - a)(x - b)^2} = \frac{A}{x - a} + \frac{B}{x - b} + \frac{C}{(x - b)^2}}$$

Repeat Quadratic Factors

$${\frac{cx + d}{(x - a)(x^2 + bx + c)^2} = \frac{A}{x - a} + \frac{Bx + C}{x^2 + bx + c} + \frac{Dx + E}{(x^2 + bx + c)^2}}$$