2. Найдите значение выражения x³y+xy³ 5(x-y) : 2(y-x) x²+y² при х=-3 и у = 1 3.

\(\frac{x^3y + xy^3}{2(y-x)} : \frac{5(x-y)}{x^2+y^2} = \frac{xy(x^2+y^2)}{2(y-x)} : \frac{5(x-y)}{x^2+y^2} =\)

\(\frac{xy(x^2+y^2)}{2(y-x)} \cdot \frac{x^2+y^2}{5(x-y)} = \frac{xy(x^2+y^2)^2}{10(y-x)^2} =\)

\(\frac{xy(x^2+y^2)^2}{10(x-y)^2}\)

Подставляем значения x = -3, y = \(\frac{1}{3}\)

\(\frac{-3 \cdot \frac{1}{3} ((-3)^2+(\frac{1}{3})^2)^2}{10(-3-\frac{1}{3})^2} = \frac{-1 (9+\frac{1}{9})^2}{10(-\frac{10}{3})^2} = \frac{-1 (\frac{82}{9})^2}{10 \cdot \frac{100}{9}} = \frac{-1 \cdot \frac{6724}{81}}{\frac{1000}{9}} = \frac{-6724 \cdot 9}{81 \cdot 1000} = \frac{-6724}{9000} = -\frac{1681}{2250}\)