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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