y=4x^2+4-4+16/(x^2+1)
=4(x^2+1)+16/(x^2+1)-4
x^2+1>=1
4(x^2+1)+16/(x^2+1)>=2根号[4(x^2+1)*16/(x^2+1)]=16
当4(x^2+1)=16/(x^2+1)时取等号
(x^2+1)^2=4
x^2=1
等号能取道
所以y>=16-4
所以最小值=12