And once again, you can feel pretty good that this is going to be your limit. We've gone back into the green zone. If you were to actually plot this original function, you would have a point discontinuity, you would have a gap at x equals four. But then when you do that simplification and factoring out that x minus, or canceling out that x minus four, that gap would disappear. And so that's essentially what you're doing. You're trying to find the limit as we approach that gap, which we got right there. Now this final one, this is dealing with trig identities.