The given expression is:

\[
\frac{4x^2 - 4x}{x - 1}
\]

We can simplify this expression step by step:

### Step 1: Factor the numerator
The numerator \(4x^2 - 4x\) has a common factor of \(4x\), so we can factor it out:

\[
4x^2 - 4x = 4x(x - 1)
\]

### Step 2: Substitute into the expression
Now, the expression becomes:

\[
\frac{4x(x - 1)}{x - 1}
\]

### Step 3: Simplify the expression
We can cancel out the common factor \((x - 1)\) in both the numerator and denominator, provided \(x \neq 1\) (to avoid division by zero):

\[
\frac{4x(x - 1)}{x - 1} = 4x \quad \text{(for } x \neq 1\text{)}
\]

Thus, the simplified expression is:

\[
4x
\]

### Conclusion:
The simplified form of the expression is \(4x\), as long as \(x \neq 1\).

Would you like more details or have any questions?

Here are some related questions for practice:
1. Simplify \(\frac{x^2 - 3x}{x - 3}\).
2. Factor and simplify \(\frac{5x^2 - 10x}{x^2 - 2x}\).
3. Simplify \(\frac{x^3 - x}{x - 1}\).
4. Simplify \(\frac{6x^2 - 18x}{3x - 9}\).
5. Factor and simplify \(\frac{2x^2 + 4x}{x + 2}\).

**Tip:** Always check for factors common to both the numerator and denominator before simplifying an algebraic expression.

Learn how to simplify the rational expression 4x^2 - 4x / (x - 1) step by step. This solution covers factoring and simplifying algebraic expressions and is suitable for students in Grades 8-10.

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