🟢 Addition:
\( \frac{2}{x} + \frac{3}{x+2} = \frac{2(x+2) + 3x}{x(x+2)} = \frac{5x + 4}{x(x+2)} \)

🔵 Subtraction:
\( \frac{x+1}{x-1} - \frac{x-2}{x+1} = \frac{(x+1)(x+1) - (x-2)(x-1)}{(x-1)(x+1)} \)

🟣 Multiplication:
\( \frac{x+2}{x-3} \times \frac{x-1}{x+5} = \frac{(x+2)(x-1)}{(x-3)(x+5)} \)

🟠 Division:
\( \frac{x^2 - 4}{x+3} \div \frac{x-2}{x-1} = \frac{(x+2)(x-1)}{x+3} \)