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

Category: QuestionsWhat form of rational function \frac{px+q}{(x-a)(x-b)}, a≠b represents?
Editor">Editor Staff asked 11 months ago

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
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

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.