Resolve into partial fractions : $\frac{x+3}{(x-1)(x+1)(x+5)}$

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Resolve into partial fractions :

$\frac{x+3}{(x-1)(x+1)(x+5)}$

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:

$\frac{x+3}{(x-1)()x+1)(x+5)}$ = $\frac{A}{x-1}$ + $\frac{B}{x+1}$ + $\frac{C}{x+5}$

therefore, x+3 = A(x+1)(x+5) +B (x-1)(x+5) +C(x-1)(x+1)

put x = 1

4=A(2)(6)

4=12A

hence, A = $\frac{1}{3}$

put x = -1

-1 + 3 = B(-2)(4)

2 = -8B

hence, B = $-\frac{1}{4}$

put x = -5

-5 + 3 = C(-6)(-4) …

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