1. Stating the problem: Solve for $x$ in the equation $$\frac{8}{x-6} = \frac{5}{x+6}$$. 2. To solve equations with fractions, we use cross-multiplication: multiply both sides by the denominators to eliminate fractions. 3. Cross-multiply: $$8(x+6) = 5(x-6)$$ 4. Expand both sides: $$8x + 48 = 5x - 30$$ 5. Move all terms involving $x$ to one side and constants to the other: $$8x - 5x = -30 - 48$$ 6. Simplify both sides: $$3x = -78$$ 7. Divide both sides by 3 to isolate $x$: $$x = \frac{-78}{3}$$ 8. Simplify the fraction: $$x = -26$$ Final answer: $$x = -26$$