a/(a^2+a+1)=1/8
1/(a+1/a+1)=1/8
a+1/a+1=8
a+1/a=7
a^2/(a^4+a^2+1)
=1/(a^2+1/a^2+1)
=1/[(a+1/a)^2-1]
=1/(7^2-1)
=1/48