1. **Stating the problem:** Solve the equation $$\frac{4}{x+1} - \frac{3}{x-1} = \frac{2}{x^2-1}$$ where $x^2-1 = (x+1)(x-1)$. 2. **Formula and rules:** To solve equations with fractions, find the least common denominator (LCD) and multiply both sides to clear denominators. Here, the LCD is $$(x+1)(x-1)$$. Important: $x \neq \pm 1$ to avoid division by zero. 3. **Multiply both sides by the LCD:** $$ (x+1)(x-1) \left( \frac{4}{x+1} - \frac{3}{x-1} \right) = (x+1)(x-1) \cdot \frac{2}{(x+1)(x-1)} $$ 4. **Simplify each term:** $$ 4 \cancel{(x+1)} (x-1)/\cancel{(x+1)} - 3 (x+1) \cancel{(x-1)}/\cancel{(x-1)} = 2 $$ which simplifies to $$ 4(x-1) - 3(x+1) = 2 $$ 5. **Expand and simplify:** $$ 4x - 4 - 3x - 3 = 2 $$ $$ (4x - 3x) + (-4 - 3) = 2 $$ $$ x - 7 = 2 $$ 6. **Solve for $x$:** $$ x = 2 + 7 $$ $$ x = 9 $$ 7. **Check restrictions:** $x \neq \pm 1$, and $9$ is allowed. **Final answer:** $$ \boxed{9} $$