1. Problem: Simplify the rational expression $\frac{6x^2 y^2}{8xy^5}$. 2. Formula and rules: To simplify a fraction, divide numerator and denominator by their greatest common factor (GCF). For variables, subtract exponents when dividing powers with the same base. 3. Work: $$\frac{6x^2 y^2}{8xy^5} = \frac{6}{8} \times \frac{x^2}{x} \times \frac{y^2}{y^5}$$ $$= \frac{3}{4} \times x^{2-1} \times y^{2-5} = \frac{3}{4} x y^{-3} = \frac{3x}{4y^3}$$ 4. Explanation: We reduced coefficients by dividing 6 and 8 by 2, subtracted exponents of $x$ and $y$ in numerator and denominator, and rewrote negative exponent as denominator. Final answer: $\frac{3x}{4y^3}$