## anonymous one year ago What is the vertical asymptote for the graph of y = x-2/(x-2)(x+3)?

1. anonymous

i think that its x=-3 and x=2 ? right?

2. mathmate

There is an ambiguity with the rational function, not sure if it is $$\large y = \frac{x-2}{(x-2)(x+3)}$$ or $$\large y = \frac{(x-2)}{(x-2)}(x+3)$$ According to the rule PEMDAS, it's the second, but I think you meant the first.

3. mathmate

Hint: simplify the rational function before attempting to locate asymptotes.

4. anonymous

It's the first equation

5. mathmate

Good, so follow the hints and see where they take you!

6. anonymous

I did simplify thats how I got x = -3

7. mathmate

What is the simplified version of the function, and what do you think the graph looks like?

8. anonymous

i think there is a hole so the answer might be (2, 1/5) ?

9. mathmate

Very good, the hole is at (2,1/5). Where do you think the asymptotes are?

10. mathmate

The function is now: f(x)=1/(x+3) where x$$\ne$$2 the hole (x=2) is not part of the domain.

11. mathmate

hint: Try to visualize where the asymptotes should be. If not ,use your graphs calculator

12. mathmate

Remember that an asymptote occurs when the denominator becomes zero.