Question

Describe the vertical asymptotes and holes for the graph of y=(x-5)/(x^2+4x+3)

Answer 1

\[y=\frac{ x-5 }{x ^{2} +4x+3}\]

Answer 2

what do u mean by describe

Answer 3

Factor the denominator:
x^2 + 4x + 3
= x^2 + x + 3x + 3
= x(x + 1) + 3(x + 1)
= (x + 3)(x + 1)
Since the numerator and denominator have no common factors, there are no holes.
To find vertical asymptotes, the denominator must be zero (and the numerator must be non-zero):
(x + 3)(x + 1) = 0
x + 3 = 0 or x + 1 = 0
x = -3 or x = -1
The answer is asymptotes: x = –3, –1 and no holes.

Answer 4

Idk, that's what the problem asks but its asking what the answers are

Answer 5

Thank you! @seiga That's what I thought for the asymptotes but I wasn't sure on how to get the holes

Answer 6

no problem(: