Question

Describe the vertical asymptote(s) and hole(s) for the graph of y=(x-3)(x+2)/(x+2)(x+3)

Answer 1

Vertical asymptotes and holes both come from values of x that make the denominator undefined. The difference between the two is whether or not a factor of the denominator cancels out with the numerator. So you have a denomiator with factors of (x+2) and (x+3). So the undefined x values would be -2 and -3 once you set each factor equal to 0. Now we look at which of those factors cancels out with the numerator, in which case the (x+2) factor does. When a factor cancels out with the numerator, the undefined x-value is a hole in the graph. When the factor does not cancel out with something in the numerator, the undefined x-value is an asymptote. So you have -2 and -3 as undefined x-values, x = -2, since it cancels with the numerator, would be a hole, and x = -3, since it does not cancel with anything in the numerator, would be an asymptote.

Answer 2

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Answer 3

Yeah, what else do you have?

Answer 4

Can I send you a message?

Answer 5

If you want.

Answer 6

I sent you the message, thank you so much