Floating point arithmetic on division
I don't know exactly where you're trying to get to with this, but I think you probably want to Taylor expand the division:

$$\frac{1}{1 - \delta_2} = 1 + \delta_2 + \delta_2^2 + \delta_2^3 + \cdots$$

Then, for example, if $\epsilon$ is the machine epsilon and $\delta_2 &gt; 0$:

$$1 + \delta_2 \le \frac{1}{1 - \delta_2} \le 1 + \delta_2 + \epsilon$$

That is quite a tight bound, when you think about it. (Exercise: Prove that this is true if $\delta_2 \le 0$, too.)