Question

2x²+x+1/(x-1)²(X+1) into partial fraction

Answer 1

Step-by-step explanation:

(x^2 + 1)/(x-1)^2.(x+1)

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

=[A(x-1)(x+1) + B(x+1) + C(x-1)^2]/(x+1)(x-1)^2

=[A(x^2 - 1) + B(x+1) + C(x^2 - 2x +1)]/(x+1)(x-1)^2

=[(A+C)x^2 + (B-2C)x + (-A+B+C)]/(x+1)(x-1)^2

A+C = 1 ………(1)

B-2C = 0 ……..(2)

-A+B+C = 1……(3)

(1)+(3) : B + 2C = 2 …..(4)

(2)+(4) : 2B = 2 ===> B=1

Subst B in (2) : 1 - 2C = 0 ===> C = 1/2.

C in (1) : A + 1/2 = 1 ===> A = 1/2.

(x^2 + 1)/(x+1)(x-1) = (1/2)/(x-1) + 1/(x-1)^2 + (1/2)/(x+1).