Which one of the following is the correct general partial–fraction form of a proper…

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Which one of the following is the correct general partial–fraction form of a proper rational function whose denominator is

(x-3)^3

? (a)

\dfrac{A}{x-3}+\dfrac{B}{(x-3)^3}

(b)

\dfrac{A(x-3)+B}{(x-3)^3}

(c)

\dfrac{A}{x-3}+\dfrac{B}{(x-3)^2}+\dfrac{C}{(x-3)^3}

(d)

\dfrac{A}{x-3}+\dfrac{B}{(x-3)^2}