Answer :
(x+2)/{(x+1)(x²+1)} = A / (x+1) + (Bx+C)/{x²+1}
= (Ax²+1+Bx²+Bx+Cx+C)/{(x+1)(x²+1)}
on comparing the coefficient of both side of same power
A+B = 0
B+C = 1
A+C = 2
A =1/2 ; B =-1/2 ; C= 3/2
put the value of A,B,C
= 1/2{1/(x+1) + (3-x)/(x²+1)}
= (Ax²+1+Bx²+Bx+Cx+C)/{(x+1)(x²+1)}
on comparing the coefficient of both side of same power
A+B = 0
B+C = 1
A+C = 2
A =1/2 ; B =-1/2 ; C= 3/2
put the value of A,B,C
= 1/2{1/(x+1) + (3-x)/(x²+1)}