The uploaded image contains several mathematical problems that you might want help solving. Let's go through each:

1. Solution of $\frac{x-7}{x-2} = \frac{x+2}{x+3}$
2. Determine the value of $k$ such that $\frac{x+5}{x+3} = \frac{x-1}{x-k}$
3. Simplify the expression $(2+3i)(2-3i)$
4. Factor the equation $x^4 - 1 = 0$ into complex factors
5. Simplify $\left( \frac{3}{x-1} - \frac{2}{x+1} \right)^2$

I will begin by solving the first problem: $\frac{x-7}{x-2} = \frac{x+2}{x+3}$. Let's solve this equation first.