Show the step by step solution on how to get the answer of 1over 2√2x-1 multiply by 2

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!

Learn how to simplify the expression 1 over 2 square root of 2x - 1 multiplied by 2 step by step. This problem involves algebraic fraction simplification and square roots, suitable for advanced high school students.

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