Solve Simple Limit Problem: (1/x)-(1/2)÷(x-2)

[swears]

lim x=>2

(1/x) - (1/2)
------------
x-2I 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!

 

[arildno]

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

 

[HallsofIvy]

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?

 

[swears]

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

No, never heard of him, sorry.

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?

I only see a common numerator of 1 not denominator.

Can I do this:

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

 

[arildno]

No, never heard of him, sorry.



I only see a common numerator of 1 not denominator.

Can I do this:

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

HORROR OF HORRORS!

NEVER EVER MISTREAT FRACTIONS IN THAT MANNER!

 

[swears]

umm, OK.

Can someone else help me out?

 

[arildno]

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

 

[swears]

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

 

[arildno]

No. You have completely misunderstood it.

 

[swears]

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

 

[arildno]

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

 

[swears]

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

 

[arildno]

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

 

[swears]

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

2 fractions

 

[arildno]

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

 

[swears]

-"this message is too short"- 1?

 

[vladimir69]

i'll give you a hint or two
$$\frac{\frac{1}{x} - \frac{1}{2}}{x-2}$$
$$=\frac{\frac{2}{2x} - \frac{x}{2x}}{x-2}$$
$$=\frac{\frac{2-x}{2x}}{x-2}$$
$$=\frac{\frac{-(x-2)}{2x}}{x-2}$$
$$=-\frac{1}{2x}$$
then substitue x=2 in there to get your answer of -.25
where i have used the following
$$\frac{\frac{a}{b}}{c}=\frac{a}{bc}$$
$$2-x=-(x-2)$$
$$\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}$$
$$\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$$

 

[swears]

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

 

[Math Is Hard]

Here is a little fraction review that might be helpful:
http://www.purplemath.com/modules/fraction4.htm

 

[vladimir69]

yeah you can do that because for example
$$\frac{1\times 2}{2\times 2} = \frac{2}{4}=\frac{1}{2}$$

 

[swears]

Cool, Thanks so much. I totally forgot about that Lowest Common Denominator thing.