2. $\frac{3 x}{x-5}=\frac{2}{x+3}$
\boxed{Final Answer: x = -\frac{7}{6} - \frac{\sqrt{71}i}{6}, x = -\frac{7}{6} + \frac{\sqrt{71}i}{6}}
Step 1 :Cross-multiply: 3x(x+3) = 2(x-5)
Step 2 :Simplify and solve for x: x = \( -\frac{7}{6} - \frac{\sqrt{71}i}{6} \), x = \( -\frac{7}{6} + \frac{\sqrt{71}i}{6} \)
Step 3 :\boxed{Final Answer: x = -\frac{7}{6} - \frac{\sqrt{71}i}{6}, x = -\frac{7}{6} + \frac{\sqrt{71}i}{6}}