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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.

Solve the given set of mathematical problems including algebraic equations, complex number operations, and conversions between different forms of complex numbers.

Explore solutions for algebraic equations, complex number operations including multiplication, simplification, and polar form conversion. This guide covers key concepts such as cross-multiplication, factoring, and complex number theorems, suitable for students in Grades 10-12.

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