因为a/(a²+1)=1/5
所以a²+1=5a
a²=5a-1
所以
a²/(a的四次方+a²+1)
=a²/(25a²-10a+1+a²+1)
=a²/(26a²-10a+2)
=a²/(130a-26-10a+2)
=a²/24(5a-1)
=a²/24a²
=1/24
因为a/(a²+1)=1/5
所以a²+1=5a
a²=5a-1
所以
a²/(a的四次方+a²+1)
=a²/(25a²-10a+1+a²+1)
=a²/(26a²-10a+2)
=a²/(130a-26-10a+2)
=a²/24(5a-1)
=a²/24a²
=1/24