Question

What form of rational function \(\frac{px+q}{(x-a)(x-b)}\), a≠b represents?

(a) \(\frac{A}{(x-a)}\)

(b) \(\frac{B}{(x-b)}\)

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

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

This question was posed to me in an online quiz.

My question is based upon Integration by Partial Fractions topic in section Integrals of Mathematics – Class 12

Answer 1

Right option is (d) \(\frac{A}{(x-a)} + \frac{B}{(x-b)}\)

Easiest explanation: The given function \(\frac{px+q}{(x-a)(x-b)}\), a≠b can also be written as

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