how do you get the horizontal asympote algibraically

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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=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.