Resolve (x/(x+1)(x-1)2) into partial fractions.

Question

Resolve (x/(x+1)(x-1)2) into partial fractions. (A) (1/2(x-1)2)+(1/4(x-1))+(1/4(x+1)) (B) (-1/4(x+1))+(1/4(x-1))+(1/2(x-1)2) (C) (-1/4(x-1))+(1/4(x+1))+(1/2(x-1)2) (D) None of these

Tardigrade Admin · Accepted Answer

(x/(x+1)(x-1)2)=(A/x+1)+(B/x-1)+(C/(x-1)2).

Q. Resolve $\frac{x}{( x + 1 ) ( x - 1 ) ^{2}}$ into partial fractions.

$\frac{1}{2 ( x - 1 ) ^{2}} + \frac{1}{4 ( x - 1 )} + \frac{1}{4 ( x + 1 )}$

$\frac{- 1}{4 ( x + 1 )} + \frac{1}{4 ( x - 1 )} + \frac{1}{2 ( x - 1 ) ^{2}}$

$\frac{- 1}{4 ( x - 1 )} + \frac{1}{4 ( x + 1 )} + \frac{1}{2 ( x - 1 ) ^{2}}$

None of these

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

Q. Resolve (x+1)(x−1)2x​ into partial fractions.

2(x−1)21​+4(x−1)1​+4(x+1)1​

4(x+1)−1​+4(x−1)1​+2(x−1)21​

4(x−1)−1​+4(x+1)1​+2(x−1)21​