Which of the following expresses the rational function as a sum of simpler fractions…

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

Problem

Which of the following expresses the rational function

\displaystyle\frac{3x+5}{(x-2)(x+1)}

as a sum of simpler fractions whose denominators are the linear factors

x-2

and

x+1

? (a)

\displaystyle\frac{Ax+B}{x-2}+\frac{C}{x+1}

(b)

\displaystyle\frac{A}{x-2}+\frac{B}{x+1}

(c)

\displaystyle\frac{A}{(x-2)(x+1)}+\frac{B}{x+1}

(d)

\displaystyle\frac{A}{x-2}+\frac{B}{(x+1)^2}