Simplify the expression \(((2x) ( 1)/((2x)) - 1 )x3\) for the limit as x approaches 0, showing the intermediate step \(((2x) (1 - (2x)))/(x3 (2x))\).

We can rewrite 1 as $\frac{\cos(2x)}{\cos(2x)}$.

$$\frac{1}{\cos(2x)} - \frac{\cos(2x)}{\cos(2x)}$$

The original expression was:

$$\lim_{x \to 0} \frac{\sin(2x) \left( \frac{1}{\cos(2x)} - 1 \right)}{x^3}$$

Replacing the parenthesis with the simplified form:

$$\lim_{x \to 0} \frac{\sin(2x) \left( \frac{1 - \cos(2x)}{\cos(2x)} \right)}{x^3}$$

The $\cos(2x)$ from the simplified parenthesis term moves to the denominator of the entire fraction:

$$\lim_{x \to 0} \frac{\sin(2x) (1 - \cos(2x))}{x^3 \cos(2x)}$$

This is the step shown in your image.