How many vertical asymptotes does the graph of \(\frac{x-3}{x^2+7x-30}\) have?

I set the denominator equal to 0 and found that x = 3, and x = -10. I thought this meant the answer to the question was 2, but it was wrong. Thanks in advance.

Guest Mar 30, 2018

#1**+2 **

x - 3

_____________

x^2 + 7x - 30

Notice that the denominator factors as

( x - 3 ) 1

______________ = _____

(x - 3) ( x + 10) x + 10

We will have a vertical asymptote at x + 10 = 0 ⇒ x = -10

And we will have a "hole" at x -3 = 0 ⇒ x = 3

See the graph, here : https://www.desmos.com/calculator/skml1smvwr

[The hole doesn't show....but. trust me...there * is* one at x = 3 !!! ]

CPhill
Mar 30, 2018