3 + x + 3 - x 3 + x - 3 - x = 2 , then x is equal to?

Answer: Option B

$$\begin{array}{rl}& \frac{\sqrt{3+x}+\sqrt{3-x}}{\sqrt{3+x}-\sqrt{3-x}}=\frac{2}{1}\\ & \Rightarrow \frac{\sqrt{3+x}}{\sqrt{3-x}}=\frac{2+1}{2-1}=\frac{3}{1}\\ & \left[\frac{\text{A}}{\text{B}}=\frac{\text{C}}{\text{D}}\right]\\ & \left[\frac{\text{A}+\text{B}}{\text{A}-\text{B}}=\frac{\text{C}+\text{D}}{\text{C}-\text{D}}\right]\\ & \Rightarrow \frac{\sqrt{3+x}}{\sqrt{3-x}}=3\\ & \text{Squaring both sides}\\ & \Rightarrow \frac{3+x}{3-x}=9\\ & \Rightarrow 3+x=27-9x\\ & \Rightarrow 10x=24\\ & \Rightarrow x=\frac{24}{10}\\ & \Rightarrow x=\frac{12}{5}\end{array}$$