# Simple Limit Problem

1. Jun 4, 2006

### swears

lim x=>2

(1/x) - (1/2)
------------
x-2

I was looking through my notes and found this problem. It shows the answer to be -.25, but I don't see how they got that. I know I want to cancel out the (x-2) on both sides of the division bar, but I'm not sure how to do this. Can anyone help me out? Thanks!

2. Jun 4, 2006

### arildno

Have you learnt about L'hopital's rule yet?
If you haven't, let your first step be to write your numerator as a single fraction.

3. Jun 4, 2006

### HallsofIvy

Staff Emeritus
L'Hopital's rule is "overkill" here!

Arildno's second suggestion, writing
$$\frac{1}{x}- \frac{1}{2}$$
as a single fraction is best. What is the common denominator?

4. Jun 4, 2006

### swears

No, never heard of him, sorry.

I only see a common numerator of 1 not denominator.

Can I do this:

$$\frac{-1}{x-2}$$ ?

Last edited: Jun 4, 2006
5. Jun 4, 2006

### arildno

HORROR OF HORRORS!!!!!!!!

NEVER EVER MISTREAT FRACTIONS IN THAT MANNER!

6. Jun 4, 2006

### swears

umm, OK.

Can someone else help me out?

7. Jun 4, 2006

### arildno

Do you even know what a fraction is, or what the symbol x stands for?

8. Jun 4, 2006

### swears

yes, x is a variable. 1/2 is a fraction.

9. Jun 4, 2006

### arildno

No. You have completely misunderstood it.

10. Jun 4, 2006

### swears

Riight. Well, are you going to correct me, or just keep criticizing?

11. Jun 4, 2006

### arildno

Why don't you sit back and re-think how we add or subtract fractions together?

12. Jun 4, 2006

### swears

I've been looking at this problem for an hour, I obviously don't know how to do it.

13. Jun 4, 2006

### arildno

Look at $\frac{1}{x}-\frac{1}{2}$
How many fractions do you have in this expression?

14. Jun 4, 2006

### swears

2 fractions

15. Jun 4, 2006

### arildno

Correct!
Now, what is a common denominator for those fractions?

16. Jun 4, 2006

### swears

-"this message is too short"- 1?

17. Jun 4, 2006

i'll give you a hint or two
$$\frac{\frac{1}{x} - \frac{1}{2}}{x-2}$$
$$=\frac{\frac{2}{2x} - \frac{x}{2x}}{x-2}$$
$$=\frac{\frac{2-x}{2x}}{x-2}$$
$$=\frac{\frac{-(x-2)}{2x}}{x-2}$$
$$=-\frac{1}{2x}$$
where i have used the following
$$\frac{\frac{a}{b}}{c}=\frac{a}{bc}$$
$$2-x=-(x-2)$$
$$\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}$$
$$\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$$

Last edited: Jun 4, 2006
18. Jun 4, 2006

### swears

Thanks for your help. I'm going to try and soak this in and figure out how u did that.

Last edited: Jun 4, 2006
19. Jun 4, 2006

### Math Is Hard

Staff Emeritus
20. Jun 4, 2006

$$\frac{1\times 2}{2\times 2} = \frac{2}{4}=\frac{1}{2}$$