since you know asymptote meaning your value be undefined; any number divided by 0. for eg: y = 1/x
make denominator add upto 0. it gives y=1/0. = undefined.
2nd eg: y = 4/(x+1)
once again, you want to make denominator add upto 0.
x= -1 (which is your horizontal asymptote)
so if you substitute back this number to the equation, you will get your denominator as zero that proves your answer is correct.