Упростите выражение: (4-3y)/(y+4):((4-y)/(y+4)+y/(y-4)).

Ответ:

\[\frac{4 - 3y}{y + 4}\ \ :\left( \frac{4 - y^{\backslash y - 4}}{y + 4} + \frac{y^{y + 4}}{y - 4} \right) =\]

\[= \frac{4 - 3y}{y + 4}\ \ :\frac{4y - y^{2} - 16 + 4y + y^{2} + 4y}{(y + 4)(y - 4)} =\]

\[= \frac{4 - 3y}{y + 4}\ \ :\frac{12y - 16}{(y + 4)(y - 4)} =\]

\[= \frac{(4 - 3y)(y + 4)(y - 4)}{(y + 4) \cdot 4(3y - 4)} =\]

\[= - \frac{y - 4}{4} = \frac{4 - y}{4}.\]