Resolve into partial fraction $\frac{x^{3}- x + 3}{(x-2)(x^{2}+1)}$

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Resolve into partial fraction

$\frac{x^{3}- x + 3}{(x-2)(x^{2}+1)}$

written 5.6 years ago by

teamques10 ★ 69k

modified 3.0 years ago by

pedsangini276 • 4.8k

engineering mathematics

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written 5.6 years ago by

teamques10 ★ 69k

Solution:

$\frac{x^{2}- x + 3}{(x - 2)(x^{2}+1)} = \frac{A}{x-2} + \frac{Bx+C}{x^{2}+1}$

$x^{2} - x +3 = (x^{2}+1)A+(x-2)(Bx+C)$

Put x=2

5 = 5A

A = 1

put x = 0

3 = A - 2C

C = 1

put x = 1

3 = 2A + (-1)(B+C)

3 = 2 - …

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