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.