Найдите значение выражения \(\frac{xу + y^2}{8x} - \frac{4x}{x + y}\) при \(x = \sqrt{3}\), \(y = -5,2\).

\[\frac{xy + y^2}{8x} - \frac{4x}{x + y} = \frac{y(x + y)}{8x} - \frac{4x}{x + y} = \frac{y(x + y)^2 - 32x^2}{8x(x + y)}\]

\[\frac{-5,2(\sqrt{3} - 5,2)^2 - 32(\sqrt{3})^2}{8\sqrt{3}(\sqrt{3} - 5,2)} = \frac{-5,2(3 - 10,4\sqrt{3} + 27,04) - 32 \cdot 3}{8\sqrt{3}(\sqrt{3} - 5,2)} = \frac{-5,2(30,04 - 10,4\sqrt{3}) - 96}{8\sqrt{3}(\sqrt{3} - 5,2)} = \frac{-156,208 + 54,08\sqrt{3} - 96}{24 - 41,6\sqrt{3}} = \frac{-252,208 + 54,08\sqrt{3}}{24 - 41,6\sqrt{3}}\]

\[\frac{(-252,208 + 54,08\sqrt{3})(24 + 41,6\sqrt{3})}{(24 - 41,6\sqrt{3})(24 + 41,6\sqrt{3})} = \frac{-6052,992 - 10492,0448\sqrt{3} + 1298,304\sqrt{3} + 6652,7232}{576 - 5205,7088} = \frac{600 - 9193,7408\sqrt{3}}{-4629,7088}\]

\[ \approx \frac{-6052,992 + 6652,7232 + (-10492,0448 + 1298,304) \sqrt{3}}{576 - (41,6)^2 \cdot 3} = \frac{599,7312 - 9193,7408 \sqrt{3}}{576 - 5205,7088} = \frac{599,7312 - 9193,7408 \sqrt{3}}{-4629,7088}\]

\[ \approx \frac{599,7312 - 9193,7408 \cdot 1,732}{-4629,7088} = \frac{599,7312 - 15923,2648}{-4629,7088} = \frac{-15323,5336}{-4629,7088} \approx 3,31 \]