I need help with vertical and horizental asymptotes

Question

(x-3)/(x+3)

x^2/(x^2-9)

(1-x^2)/(x^2-2x+1)

(x^2-4)/(x^4-16)

x(x-1)(x-2)/(x^4-x^2)

Answer 1

vertical where denominator is zero and numerator is not. So, for
x(x-1)(x-2)/(x^4-x^2)
the denominator x^2(x-2)(x+2)
But the numerator is also zero at x=0,2 so the only vertical asymptote is at x = -2. There are holes at x=0,2

Horizontal asymptotes occur where
y=0 if the degree of the top is less than the bottom, as is the case of the last two functions.

Otherwise, take the coefficients of the highest power, and the asymptote is the ratio of top/bottom. As x gets huge, only the highest power matters.
Since all these coefficients are -1 or 1, this is quite easy for the first three functions.

I'm sure all this is explained in your class material. google for may more examples and discussions.