Discuss the asymptotes and concavity of the function y=x²÷x-1

as x-->inf y~x^2/x=x
y=x is an asymptote of the function
y'=2x(x-1)-x^2/(x-1)^2 = x^2-2x
y'=0 gives x(x-2)=0 , x=0 and x=2
for x>2 and x<0 function increasing , and between (0,2 ) function is decreasing.
sher mohammad
b.tech, iit delhi

as x-->inf y~x^2/x=x y=x is an asymptote of the function y`=2x(x-1)-x^2/(x-1)^2 = x^2-2x y`=0 gives x(x-2)=0 , x=0 and x=2 for x>2 and x<0 function increasing , and between (0,2 ) function is decreasing.