Упростите выражение: (y+3)/(2y+2)-(y+1)/(2y-2)+3/(y^2-1).

Ответ:

\[\frac{y + 3}{2y + 2} - \frac{y + 1}{2y - 2} + \frac{3}{y^{2} - 1} =\]

\[= \frac{y + 3^{\backslash y - 1}}{2(y + 1)} - \frac{y + 1^{\backslash y + 1}}{2(y - 1)} + \frac{3^{\backslash 2}}{(y - 1)(y + 1)} =\]

\[= \frac{y^{2} + 3y - y - 3 - y^{2} - 2y - 1 + 6}{2(y - 1)(y + 1)} =\]

\[= \frac{2}{2\left( y^{2} - 1 \right)} = \frac{1}{y^{2} - 1}.\]