Question

Resolve into pontial fraction (x ^ 3 + x)/(x ^ 2 - 4)​

Answer 1

(x^3+x)/(x^2-4)=(x^3+X)/{(X+4)(x-4)}

(x^3+x) /(x^2-4) = A/(X+4) +B/((x-4)

=A(x-4)+B(X+4)/(x^2-4)

x^3+X=A(x-4)+B(X+4)

put X=4 we get 64+4= A(0)+B(8)

68/8 =B

B= 17/2

put X= -4 we get -64-4 = -8A

-68/-8 =A

A=17/2

(x^3+x)/(x^2-4) = 17/2(X+4) + 17/2(x-4)