Here’s the English translation of your question: **"If \( x = \frac{4ab}{a + b} \), then what is the value of \( \frac{x + 2a}{x - 2a} + \frac{x + 2b}{x - 2b} \)?"** Would you like me to solve it step by step?

Q.Here’s the English translation of your question: **"If \( x = \frac{4ab}{a + b} \), then what is the value of \( \frac{x + 2a}{x - 2a} + \frac{x + 2b}{x - 2b} \)?"** Would you like me to solve it step by step? (a) 1 (b) -2 (c) 2 (d) -1

Answer: C

Given: \[ x = \frac{4ab}{a + b} \] Then, \[ \frac{x}{2a} = \frac{2b}{a + b} \Rightarrow \frac{x + 2a}{x - 2a} = \frac{2b + a + b}{2b - a - b} = \frac{a + 3b}{b - a} \] Again, \[ \frac{x}{2b} = \frac{2a}{a + b} \Rightarrow \frac{x + 2b}{x - 2b} = \frac{2a + a + b}{2a - a - b} = \frac{3a + b}{a - b} \] Therefore, \[ \frac{x + 2a}{x - 2a} + \frac{x + 2b}{x - 2b} = \frac{a + 3b}{b - a} + \frac{3a + b}{a - b} = \frac{a + 3b}{b - a} - \frac{3a + b}{b - a} = \frac{a + 3b - 3a - b}{b - a} = \frac{2b - 2a}{b - a} = \frac{2(b - a)}{b - a} = 2 \]