https://file.aiquickdraw.com/mathbot/file/1726756393464q9ml8tjk.jpg

The expression shown in the image is:

\[
\frac{x+2}{x-6} \cdot \frac{3x^2}{x^2 + 4x + 4}
\]

Let's simplify this step by step:

### Step 1: Factor the quadratic denominator
The second denominator is \( x^2 + 4x + 4 \), which can be factored as a perfect square trinomial:

\[
x^2 + 4x + 4 = (x+2)^2
\]

### Step 2: Rewrite the expression
Now, the expression becomes:

\[
\frac{x+2}{x-6} \cdot \frac{3x^2}{(x+2)^2}
\]

### Step 3: Simplify the common terms
We can cancel one factor of \( x+2 \) from both the numerator and denominator:

\[
\frac{1}{x-6} \cdot \frac{3x^2}{x+2} = \frac{3x^2}{(x-6)(x+2)}
\]

### Final Expression:
Thus, the simplified form of the expression is:

\[
\frac{3x^2}{(x-6)(x+2)}
\]

Let me know if you would like further details or explanations on this! 

Here are 5 questions for practice:
1. What would happen if \(x = -2\) in the original expression?
2. What is the domain of the simplified expression?
3. How do you factor quadratic expressions like \(x^2 + 4x + 4\)?
4. What are the possible restrictions on \(x\) due to the denominators?
5. How would the result change if the expression included subtraction instead of multiplication?

**Tip**: Always check for factoring opportunities in both the numerator and the denominator when simplifying rational expressions.

Simplify the expression: (x + 2) / (x - 6) * (3x^2) / (x^2 + 4x + 4)

Learn how to simplify rational expressions step by step by factoring quadratic expressions and canceling common terms. This problem covers essential algebraic concepts for students in Grades 9-11, including simplifying fractions and factoring quadratics.

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