Question

how to describe vertical asymptotes and holes for the graph

y= (x-2)(x+4)/(x+4)(x+5)

Answer 1

holes occur at the points that the top and bottom cancel:

(x+4)
----- in this case; there is a hole at x = -4
(x+4)

VAs occur when you cant cancel; which in this case is x = -5

Answer 2

why wouldnt the (x-2) be a asymtote?

Answer 3

x-2 makes 0 up top which is perfectly acceptable; asmps and holes are were the domain is undefined

Answer 4

0/# is fine

#/0 is bad;

#/0 is either a asymp or a hole