To solve the expression $\frac{1}{2\sqrt{2x - 1}} \times 2$, we'll go through the process step by step.

Step 1: Write Down the Expression

The expression given is: $\frac{1}{2\sqrt{2x - 1}} \times 2$

Step 2: Simplify the Multiplication

To simplify the expression, multiply the fraction by 2: $\frac{1 \times 2}{2\sqrt{2x - 1}} = \frac{2}{2\sqrt{2x - 1}}$

Step 3: Simplify the Fraction

Notice that the numerator (2) and the denominator (2) can cancel each other out: $\frac{2}{2\sqrt{2x - 1}} = \frac{1}{\sqrt{2x - 1}}$

Final Answer

So, the simplified expression is: $\frac{1}{\sqrt{2x - 1}}$

Would you like more details or have any questions about this solution?

Here are some related questions you might find useful:

1. How do you rationalize the denominator of $\frac{1}{\sqrt{2x - 1}}$?
2. What is the derivative of $\frac{1}{\sqrt{2x - 1}}$?
3. How do you solve an equation involving $\frac{1}{\sqrt{2x - 1}} = k$ for $x$?
4. What happens if $2x - 1$ is negative in the context of the original expression?
5. How does the original expression change if it's instead $\frac{1}{2\sqrt{2x + 1}} \times 2$?

Tip: Always simplify fractions as much as possible to make calculations easier and clearer!