1. **State the problem:** Solve the equation $$\frac{1}{\tanh(x)} - \frac{0.5}{\tanh(x)} - \frac{0.95}{x} = 0$$ for $x$. 2. **Combine like terms:** Since the first two terms have the same denominator $\tanh(x)$, combine them: $$\frac{1 - 0.5}{\tanh(x)} - \frac{0.95}{x} = 0$$ which simplifies to $$\frac{0.5}{\tanh(x)} - \frac{0.95}{x} = 0$$ 3. **Isolate terms:** Move the second term to the right side: $$\frac{0.5}{\tanh(x)} = \frac{0.95}{x}$$ 4. **Cross multiply:** $$0.5 x = 0.95 \tanh(x)$$ 5. **Rewrite the equation:** $$0.5 x - 0.95 \tanh(x) = 0$$ 6. **Interpretation:** This is a transcendental equation involving $x$ and $\tanh(x)$, which generally requires numerical methods to solve. 7. **Numerical solution approach:** Use methods like Newton-Raphson or graphing to find $x$ such that $$0.5 x = 0.95 \tanh(x)$$ 8. **Approximate solution:** By testing values, $x \approx 1.5$ satisfies the equation closely. **Final answer:** The solution to the equation is approximately $$x \approx 1.5$$.