3. Найдите значение выражения xy³-x³y 3(x-y) 2(y-x) x²-y² при х=4 и у=¹/₄

\[\begin{aligned} \frac{xy^3 - x^3y}{2(y-x)} \cdot \frac{3(x-y)}{x^2 - y^2} &= \frac{xy(y^2 - x^2)}{2(y-x)} \cdot \frac{3(x-y)}{x^2 - y^2} \\ &= \frac{xy(-(x^2 - y^2))}{2(y-x)} \cdot \frac{3(x-y)}{x^2 - y^2} \\ &= \frac{-xy(x^2 - y^2)}{2(y-x)} \cdot \frac{3(x-y)}{x^2 - y^2} \\ &= \frac{-xy \cdot 3(x-y)}{2(y-x)} \\ &= \frac{-3xy(x-y)}{-2(x-y)} \\ &= \frac{3xy}{2} \end{aligned}\]

\[\begin{aligned} \frac{3xy}{2} &= \frac{3 \cdot 4 \cdot \frac{1}{4}}{2} \\ &= \frac{3}{2} \\ &= 1.5 \end{aligned}\]