We know that ‌x4+x2+1=(x2+x+1)(x2−x+1) ‌{∴a=1} ‌‌
1
x4+x2+1
=‌
Ax+B
x2+x+1
+‌
Cx+D
x2−x+1
‌=‌
1(x2+x+1)(x2−x+1)
(x2+x+1)(x2−x+1)
‌1=(Ax+B)(x2−x+1)+(Cx+D)(x2+x+1) ‌1=Ax3−Ax2+Ax+Bx2−Bx+B ‌‌‌+Cx3+Cx2+Cx+Dx2+Dx+D On comparing, we get Coefficient of x3=0A+C=0 Coefficient of x2=0 −A+B+C+D=0 Coefficient of x=0 ‌A−B+C=0 ‌B+D=1 From Eqs. (i) and (iv), we get A−C=1 and from Eqs. (i) and (v) we get, and from Eqs. (i) and (v) we get, A=‌