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

\(\frac{4}{y}-\frac{2}{y-5}+\frac{2y}{25-y^2}-\frac{10}{y^2-25} = \frac{4}{y}-\frac{2}{y-5}-\frac{2y}{(y-5)(y+5)}+\frac{10}{(y-5)(y+5)} = \frac{4(y-5)(y+5)-2y(y+5)-2y+10}{y(y-5)(y+5)} = \frac{4(y^2-25)-2y(y+5)-2y+10}{y(y-5)(y+5)} = \frac{4y^2-100-2y^2-10y-2y+10}{y(y-5)(y+5)} = \frac{2y^2-12y-90}{y(y-5)(y+5)} = \frac{2(y^2-6y-45)}{y(y-5)(y+5)} = \frac{2(y-15)(y+3)}{y(y-5)(y+5)}\)