Help with Limit Homework Problem - Simplifying

[crybllrd]

Homework Statement

I'm having trouble with a homework problem:

$$\lim_{x\to 0}\frac{\frac{1}{3+x}-\frac{1}{3}}{x}$$

I wasn't sure how to simplify this. I tried a conjugate, but assuming I did it right, it didn't get me anywhere.

 

[micromass]

Hi crybllrd!

You may start by simplifying

$$\frac{1}{3+x}-\frac{1}{3}$$...

 

[stevenb]

Homework Statement

I'm having trouble with a homework problem:

$$\lim_{x\to 0}\frac{\frac{1}{3+x}-\frac{1}{3}}{x}$$

I wasn't sure how to simplify this. I tried a conjugate, but assuming I did it right, it didn't get me anywhere.

$$\lim_{x\to 0}{\frac{1}{3x+x^2}-\frac{1}{3x}}$$

Then combine terms with a common denominator.

You'll see it after that.

 

[crybllrd]

Thanks guys, I was making that way more difficult than it was.
I had done it the right way the first time, but I guess I made a math error because it didn't work out. I did it correctly now, though.
Thanks again!