Using ε,δ-Definition to Show $\lim_{x\to a}\frac{1}{x}=\frac{1}{a}$

[wonnabewith]

Homework Statement

The question is asking to use the ε, δ-definition of limit to show that lim x->a 1/x=1/a

Homework Equations

$$\lim_{x \to a} f(x) = L$$

The Attempt at a Solution

Here is what I have so far:
|1/x-x/a|<ε
and |x-a|<δ
I have no idea what to do next, please help
thanx

 

[QuarkCharmer]

This guy does a good job explaining it.