# Homework Help: Need help with limit question

1. Feb 24, 2012

### Johnyi

1. The problem statement, all variables and given/known data
Lim x^2-16/4-x
x→4

2. Relevant equations

3. The attempt at a solution

I factored it, and ended up with (x-4)(x+4)/(4-x)

Cant cancel anything out, so I plug in 4 back into it, and end up with 8 as the limit. But the book says that the answer is -8?

2. Feb 24, 2012

### SammyS

Staff Emeritus
What is -(x-4) ?

3. Feb 24, 2012

### Johnyi

Wouldnt that just be 0? Also why is there a - before the (x-4)?

4. Feb 24, 2012

### Staff: Mentor

Why do you think it would be zero?

Hint: Distributive property.

As a side note, if you have a hard time understanding how -(x - 4) might possibly be related to 4 - x, I think you will have a really hard time in more advanced topics such as limits.

5. Feb 24, 2012

### SammyS

Staff Emeritus
I'm not asking you to take the limit of -(x-4).

Simplify -(x-4).

Alternatively, factor a (-1) out of (x-4).

6. Feb 24, 2012

### Johnyi

Where did you get the - before the (x-4) though?

7. Feb 24, 2012

### SammyS

Staff Emeritus

It may be clear to you after that.

8. Feb 24, 2012

### Johnyi

So if i distribute the - it will be -x+4, which cancels with the denominator, and im left with x+4. I plug in 4 for x and get 8?

9. Feb 24, 2012

### SammyS

Staff Emeritus
Almost correct.

Yes, you're right about -(x-4) = -x + 4. Of course that is the same as 4 - x .

So rewrite your expression with a denominator of -(x - 4).

Do you see why I had the "-" sign out front of the (x-4) in my previous posts?

10. Feb 24, 2012

### Johnyi

Sorry..I just cant understand how the "-" sign came out of nowhere, and why i have to rewrite the denominator as -(x-4)

11. Feb 24, 2012

### SammyS

Staff Emeritus
Didn't you determine that -(x-4) is -x + 4 ?

Well, that's the same as 4 - x, which is the denominator.

4 - x is the same as -(x - 4).

So, replace the denominator, which is 4 - x, with -(x - 4) because they're equivalent.

In general, a - b = -(b - a) .

12. Feb 24, 2012

### Johnyi

So then wouldnt they both cancel anyways leaving me with just (x+4)?

13. Feb 24, 2012

### SammyS

Staff Emeritus
If the denominator is -(x-4) then there is also a "-" sign left uncancelled.