1. **State the problem:** Simplify the expression $$\frac{-15x^2ab}{12b^2x^2}$$. 2. **Write the formula and rules:** When simplifying fractions with variables and coefficients, divide the coefficients and apply the laws of exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Simplify the coefficients:** $$\frac{-15}{12} = \frac{\cancel{-15}}{\cancel{12}} = \frac{-5}{4}$$ (dividing numerator and denominator by 3). 4. **Simplify the variables:** - For $$x^2$$ in numerator and denominator: $$\frac{x^2}{x^2} = x^{2-2} = x^0 = 1$$. - For $$b$$ in numerator and $$b^2$$ in denominator: $$\frac{b}{b^2} = b^{1-2} = b^{-1} = \frac{1}{b}$$. - The variable $$a$$ remains in numerator as it has no counterpart in denominator. 5. **Combine all simplified parts:** $$\frac{-5}{4} \times 1 \times a \times \frac{1}{b} = \frac{-5a}{4b}$$. **Final answer:** $$\boxed{\frac{-5a}{4b}}$$