# Thread: Limits; (7 - x) / (x - 7) as x approaches 7: How do I SHOW that it's -1?

1. ## Limits; (7 - x) / (x - 7) as x approaches 7: How do I SHOW that it's -1?

Hello, all. I am trying to solve a limit question and although I am aware of the correct answer, I'm not quite sure how to arrive at it.

For x approaches 7, (7 - x) / (x - 7)

I know the answer is (-1), but I am not sure how to arrive there. It seems to me that both terms would cancel out and the answer would be 1.

Thanks in advance for any replies!

2. Originally Posted by BusCalc
Hello, all. I am trying to solve a limit question and although I am aware of the correct answer, I'm not quite sure how to arrive at it.

For x approaches 7, (7 - x) / (x - 7)

I know the answer is (-1), but I am not sure how to arrive there. It seems to me that both terms would cancel out and the answer would be 1.

Thanks in advance for any replies!
Hint:

x - 7 = -1 * (7 - x)

3. Originally Posted by Subhotosh Khan
Hint:

x - 7 = -1 * (7 - x)
Ahh, I see my mistake. I treated (7 - x) as though x were positive. So the (-1) is used to swap the signs of x and 7.

Thank you for taking the time to help me out! I really appreciate it.

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