a factor in the numerator is the opposite of the denominator - simplifies to -1

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I'm working on a little khan academy problem, finding the limit as x -> 36 in the solution the program explains in the last step that since there are opposite factors in the numerator and denominator, they reduce to -1

(36−x)(x√+6)/x−36 = (-1)(x√+6)

I've not encountered this situation before and I'm having a terrible time of finding resources to explain this contingency.

It's also possible that I'm just reading the problem incorrectly.

Is this in fact what is taking place? I suppose I understand the logic behind it, I'm very inexperienced so any reinforcement of this concept would be appreciated.

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1 Answer

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You are correct. The reason you result in a $-1$ is because you can factor out a $-1$ from the numerator. Let $a$ be any number. $$\frac{a-x}{x-a} = \frac{(-1)(x-a)}{x-a} = -1.$$

Tricks like these are common in solving limit problems with discontinuities.

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