1. **State the problem:** Simplify and solve the equation $$\frac{a+b}{a \times b} - \frac{a-b}{a \times b} = \frac{b}{8}$$ for $a$ and $b$. 2. **Identify the formula and rules:** Since the denominators on the left side are the same, we can combine the fractions by subtracting the numerators directly. 3. **Combine the fractions:** $$\frac{a+b}{a b} - \frac{a-b}{a b} = \frac{(a+b) - (a-b)}{a b} = \frac{a + b - a + b}{a b} = \frac{2b}{a b}$$ 4. **Simplify the fraction:** $$\frac{2b}{a b} = \frac{2}{a}$$ 5. **Set equal to the right side:** $$\frac{2}{a} = \frac{b}{8}$$ 6. **Cross multiply to solve for $a$ in terms of $b$:** $$2 \times 8 = a \times b$$ $$16 = a b$$ 7. **Interpretation:** The product of $a$ and $b$ must be 16 for the equation to hold true. **Final answer:** $$a b = 16$$