Simplifying rational expressions and not sure what to exclude

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I am studying precalculus using Khan academy and I can't figure out why my answer isn't also correct. We are to simplify

$\frac{x^2+6x+5}{x^2-x-2}$

First we factor:

$\frac{(x+1)(x+5)}{(x+1)(x-2)}$

And then we cancel the x+1:

$\frac{x+5}{x-2}$

The video linked below (around 7 minutes in) claims that x cannot equal -1 because the denominator would be zero in the second expression. Apparently this is the only exclusion. But what about x=2? That would make both the original expression and the final simpified one undefined. Why is -1 the correct answer (if it indeed is?)

https://youtu.be/7Uos1ED3KHI

Also - I graphed both the original and simplified expression as functions on a graphing calculator. Both functions show an asymptote at x=2. Doesn't that support my answer?

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