Question

Find partial decomposition of (x+6)/[x^2(x^2+2)]

Answer 1

Explanation:

`(x+6)/(x^2(x^2+2)) =(A)/(x) +(B)/(x^2) +(Cx+D)/(x^2+2) \\x+6=Ax(x^2+2)+B(x^2+2)+(Cx+D)x^2\\equating~co-efficients ~of~same~powers~of~x\\0=A+C (of~x^3)\\0=B+D (of~x^2)\\1=2A (of~x)\\A=1/2\\6=2B (constant~term)\\B=6/2=3\\C=-A=-1/2\\D=-B=-3\\(x+6)/(x^2(x^2+2)) =(1)/(2x) +(-3)/(x^2) +(-(1)/(2) x-3)/(x^2+2)`