已知a/a方+a+1=1/5求分式a方/a的4次方+5a方+1的值

a/a方+a+1=1/5
1/(a+1+1/a)=1/5
a+1/a=5-1=4

a方/a的4次方+5a方+1
=1/(a^2+5+1/a^2)
=1/[(a+1/a)^2+3]
=1/(16+3)
=1/19

已知a/a^2+a+1=1/5求分式a^2/a^4+5a^2+1的值
a/a^2+a+1=1/5取倒数
a^2+a+1/a=5
a+1+1/a=5
a+1/a=4
a^2+1/a^2=(a+1/a)^2-2=16-2=14

a^2/(a^4+5a^2+1)取倒数

(a^4+5a^2+1)/a^2
=a^2+5+1/a^2
=14+5
=19

即
a^2/(a^4+5a^2+1)=1/19