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# How many Vertical Asymptotes?

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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.

Mar 30, 2018

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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   !!!  ]

Mar 30, 2018