4. Упростите выражение \(\frac{4}{y} - \frac{2}{y-5} + \frac{2y}{25-y^2} - \frac{10}{y^2-25}\).

\(\frac{4}{y} - \frac{2}{y-5} + \frac{2y}{25-y^2} - \frac{10}{y^2-25} = \frac{4}{y} - \frac{2}{y-5} - \frac{2y}{y^2-25} + \frac{10}{y^2-25} = \frac{4}{y} - \frac{2}{y-5} + \frac{10-2y}{y^2-25} = \frac{4}{y} - \frac{2}{y-5} + \frac{2(5-y)}{(y-5)(y+5)} = \frac{4}{y} - \frac{2}{y-5} - \frac{2}{y+5} = \frac{4(y-5)(y+5) - 2y(y+5) - 2y(y-5)}{y(y-5)(y+5)} = \frac{4(y^2-25) - 2y^2-10y - 2y^2+10y}{y(y-5)(y+5)} = \frac{4y^2-100-4y^2}{y(y-5)(y+5)} = \frac{-100}{y(y-5)(y+5)}\) Ответ: \(\frac{-100}{y(y-5)(y+5)}\)