Упростите выражение 4/y-2/(y-5)+2y/(25-y^2)-10/(y^2-25).

Ответ:

\[\frac{4}{y} - \frac{2}{y - 5} + \frac{2y}{25 - y^{2}} - \frac{10}{y^{2} - 25} =\]

\[= \frac{4^{\backslash y^{2} - 25}}{y} - \frac{2^{\backslash y(y + 5)}}{y - 5} - \frac{2y}{y^{2} - 25} - \frac{10}{y^{2} - 25} =\]

\[= \frac{4 \cdot \left( y^{2} - 25 \right) - 2y(y + 5) - 2y \cdot y - 10y}{y\left( y^{2} - 25 \right)} =\]

\[= \frac{4y^{2} - 100 - \ 2y^{2} - 10y - 2y^{2} - 10y}{y\left( y^{2} - 25 \right)} =\]

\[= \frac{- 20y - 100}{y(y + 5)(y - 5)} = \frac{- 20 \cdot (y + 5)}{y(y + 5)(y - 5)} =\]

\[= \frac{- 20}{y(y - 5)} = \frac{20}{5y - y²}\]