Let's simplify the given expression step by step:

The expression is:

\[
\frac{2x^2 - 10x}{x+2} \cdot \frac{6}{2x^2 - 10x}
\]

### Step 1: Factor common terms

#### Factor the numerator \(2x^2 - 10x\) in both fractions:
\[
2x^2 - 10x = 2x(x - 5)
\]

So, the expression becomes:

\[
\frac{2x(x - 5)}{x + 2} \cdot \frac{6}{2x(x - 5)}
\]

### Step 2: Simplify the common factors

Notice that \(2x(x - 5)\) appears in both the numerator and denominator, so they cancel out:

\[
\frac{1}{x + 2} \cdot 6
\]

### Step 3: Multiply what's left
Now multiply the fractions:

\[
\frac{6}{x + 2}
\]

### Final Answer:

The simplified expression is:

\[
\frac{6}{x + 2}
\]

Would you like any further details or explanations?

Here are 5 follow-up questions to deepen understanding:
1. What happens if \(x = -2\) in the simplified expression?
2. How would you simplify if the original expression had a different denominator?
3. Can you generalize the process of canceling common factors in other rational expressions?
4. How do you handle complex fractions with polynomials in both numerator and denominator?
5. What is the importance of factoring when simplifying algebraic expressions?

**Tip:** Always check for common factors before multiplying or dividing expressions—it simplifies the work and reduces errors.

Learn how to simplify the rational expression 2x² - 10x / (x+2) • 6 / 2x² - 10x step-by-step. This solution explains factoring, cancellation of common factors, and the importance of simplifying expressions in algebra. Suitable for students in Grades 9-11.

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