Question

Which form of rational function \(\frac{px+q}{(x-a)^2}\) represents?

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

(b) \(\frac{A}{(x-a)^2} + \frac{B}{(x-a)}\)

(c) \(\frac{A}{(x-a)} – \frac{B}{(x-a)^2}\)

(d) \(\frac{A}{(x-a)} – \frac{B}{(x-a)}\)

The question was posed to me in exam.

I want to ask this question from Integration by Partial Fractions in portion Integrals of Mathematics – Class 12

Answer 1

Right option is (a) \(\frac{A}{(x-a)} + \frac{B}{(x-a)^2}\)

Best explanation: It is a form of the given partial fraction \(\frac{px+q}{(x-a)^2}\) which can also be written as

\(\frac{A}{(x-a)} + \frac{B}{(x-a)^2}\) and is further used to solve integration by partial fractions numerical.