Which of the following represents the correct general partial-fraction decomposition of ?

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

Problem

Which of the following represents the correct general partial-fraction decomposition of

\dfrac{x^{2}}{(x-1)(x^{2}+1)}

? (a)

\dfrac{A}{x-1}+\dfrac{B}{x^{2}+1}

(b)

\dfrac{A}{x-1}+\dfrac{Bx+C}{x^{2}+1}

(c)

\dfrac{A}{x-1}+\dfrac{Bx+C}{(x^{2}+1)^{2}}

(d)

\dfrac{A}{(x-1)^{2}}+\dfrac{Bx+C}{x^{2}+1}