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The image contains 10 problems involving the simplification of rational expressions. Let's begin by solving these one by one, starting with problem 1.

### Problem 1:
\[
\frac{\frac{x^2 - 4x + 4}{x^2 - 9}}{\frac{x^2 + 6x + 9}{x^2 - 4}}
\]

This expression involves division of two rational expressions, which can be simplified by multiplying by the reciprocal of the divisor.

We begin by factoring each polynomial.

1. \( x^2 - 4x + 4 = (x - 2)^2 \)
2. \( x^2 - 9 = (x - 3)(x + 3) \)
3. \( x^2 + 6x + 9 = (x + 3)^2 \)
4. \( x^2 - 4 = (x - 2)(x + 2) \)

Now rewrite the expression:

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

Next, multiply by the reciprocal of the second fraction:

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

Simplify:

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

This is the simplified form.

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Simplify rational expressions from a math worksheet involving division and multiplication of polynomials.

This worksheet focuses on simplifying rational expressions by factoring, multiplying, and dividing polynomials. Learn how to break down complex fractions and apply algebraic rules. Suitable for high school algebra students in Grades 9-12.

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