I see that you need help with problems 7 and 8 from the document. Let's break them down.

Problem 7:

Given the two expressions:

$A = \frac{\sqrt{x}}{\sqrt{x - 2}} \quad \text{and} \quad B = \frac{\sqrt{x} - 6}{\sqrt{x - 3} - x - 9}$

Task 1: Find the value of the expression $A$ when $x = 25$.

To solve this, substitute $x = 25$ into the formula for $A$:

$A = \frac{\sqrt{25}}{\sqrt{25 - 2}} = \frac{5}{\sqrt{23}}$

Thus, the value of $A$ when $x = 25$ is $\frac{5}{\sqrt{23}}$.

Task 2: Prove that:

$B = \frac{\sqrt{x - 3}}{\sqrt{x + 2}}$

This task likely requires simplifying the given expression for $B$. Let's simplify the original expression step-by-step and see if we can arrive at the desired result.

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Problem 8:

Given the two expressions:

$A = \frac{x + 3}{\sqrt{x - 2}} \quad \text{and} \quad B = \frac{\sqrt{x + 3}}{2 \sqrt{x + 4}}$

Task 1: Find the value of the expression $A$ when $x = 16$.

Substitute $x = 16$ into the formula for $A$:

$A = \frac{16 + 3}{\sqrt{16 - 2}} = \frac{19}{\sqrt{14}}$

Thus, the value of $A$ when $x = 16$ is $\frac{19}{\sqrt{14}}$.

Task 2: Simplify the expression for $B$.

To simplify $B$, we can first look at the terms:

$B = \frac{\sqrt{x + 3}}{2 \sqrt{x + 4}}$

If you'd like, I can help you simplify this expression further, but based on the structure, it looks like the form already appears simplified.

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Let me know if you'd like more details or have any specific questions! Would you like to explore any specific steps further?

Here are a few questions that expand on the current concepts:

1. How do we handle expressions involving square roots when they appear in fractions?
2. What happens when square roots appear in both the numerator and denominator?
3. How do you rationalize a denominator that contains a square root?
4. What is the significance of the value $x = 16$ in these types of expressions?
5. How does simplifying square root expressions help in solving equations efficiently?

Tip: When dealing with square roots in equations, always check if the expressions can be simplified first to make the calculations easier.