To simplify the expression \(\frac{x}{2x - 4} \times \frac{x - 2}{1}\), follow these steps:

### Step 1: Factor where possible.
We can factor the denominator \(2x - 4\) as \(2(x - 2)\). So the expression becomes:

\[
\frac{x}{2(x - 2)} \times \frac{x - 2}{1}
\]

### Step 2: Cancel common factors.
The factor \(x - 2\) appears in both the numerator and the denominator, so we can cancel it out:

\[
\frac{x}{2} \times 1 = \frac{x}{2}
\]

Thus, the simplified expression is:

\[
\frac{x}{2}
\]

Would you like further details or have any questions about this?

Here are some related questions to explore:
1. How do you simplify expressions with multiple fractions?
2. What are the rules for factoring polynomials?
3. Can you solve for \(x\) when the expression equals a certain value?
4. How does canceling out terms work in more complex fractions?
5. What if the denominator had more complex factors?

**Tip**: Always look for common factors before multiplying or dividing fractions; it makes simplifying easier!

Simplify the algebraic expression x/(2x-4) × (x-2)/1 with this step-by-step solution. Learn how to factor denominators and cancel common terms in fractions. This problem covers important concepts like factoring and simplifying rational expressions, suitable for students in Grades 9-10.

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