It looks like you've shared a math problem involving fractions and algebraic expressions. I can help you simplify and solve the expressions. Let's go through each part step-by-step.

1. Expression:
   $\frac{x+6}{x+15} \div \frac{x^2 - 25}{x - 25}$ First, you need to rewrite the division as multiplication by the reciprocal: $\frac{x+6}{x+15} \times \frac{x - 25}{x^2 - 25}$ Next, factor the quadratic expression in the denominator: $x^2 - 25 = (x - 5)(x + 5)$ Thus, the expression becomes: $\frac{x+6}{x+15} \times \frac{x-25}{(x-5)(x+5)}$ Now, simplify the expression by canceling out common terms if possible.

I'll proceed with the next expressions as well if you'd like! Would you like me to continue with these steps or break them down more clearly?