# How do you find the horizontal asymptote for y = (x-4)^2/(x^2-4)?

Feb 26, 2016

Horizontal asymptote is $y = 1$

#### Explanation:

y=(x−4)^2/(x^2−4) or y=(x^2-8x+16)/(x^2−4)

can also be simplified as y=(x−4)^2/((x+2)(x-2))

Hence vertical asymptote are $x = 2$ and $x = - 2$

Fuether, as highest degree of numerator divided by highest degree of denominator is same, and ratio is given by

${x}^{2} / {x}^{2} = 1$

Horizontal asymptote is $y = 1$