Explore topic-wise InterviewSolutions in .

This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.

1.	Resolve into partial fractions \(\frac{9}{(x + 1)(x + 2)^2}\)
Answer» Let \(\frac{9}{(x + 1)(x + 2)^2}\) = \(\frac{A}{x + 1} + \frac{B}{x + 2} + \frac{C}{(x + 2)^2}\) 9 = A(x + 2)² + B(x + 1)(x + 2) +C(x + 1) Put x = -1, 9 = A(-1 + 2)² + 0 + 0 A = 9 Put x= -2, 9 = A(0) + B(0) + C – 10 = -9 Put x = 0, 9 = 4A + 2B + C 9 = 36 + 2B -9 9 = 27 + 2B\(\frac{-18}{2}\) B = -9 \(\frac{9}{x - 1} - \frac{9}{x + 2} - \frac{9}{(x + 2)^2}\)

Resolve into partial fractions \(\frac{9}{(x + 1)(x + 2)^2}\)

Answer»

Let \(\frac{9}{(x + 1)(x + 2)^2}\) = \(\frac{A}{x + 1} + \frac{B}{x + 2} + \frac{C}{(x + 2)^2}\)

9 = A(x + 2)² + B(x + 1)(x + 2) +C(x + 1)

Put x = -1, 9 = A(-1 + 2)² + 0 + 0 A = 9

Put x= -2, 9 = A(0) + B(0) + C – 10 = -9

Put x = 0, 9 = 4A + 2B + C

9 = 36 + 2B -9

9 = 27 + 2B\(\frac{-18}{2}\) B = -9

\(\frac{9}{x - 1} - \frac{9}{x + 2} - \frac{9}{(x + 2)^2}\)

Discussion