Решебник по алгебре 8 класс Мерзляк ФГОС Задание 268

\[\boxed{\text{268\ (268).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

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

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

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

\[= \frac{5a^{2} - 10a + 5}{2 \cdot (a - 1)(a + 1)} =\]

\[= \frac{5 \cdot \left( a^{2} - 2a + 1 \right)}{2 \cdot (a - 1)(a + 1)} =\]

\[= \frac{5(a - 1)^{2}}{2 \cdot (a - 1)(a + 1)} =\]

\[= \frac{5 \cdot (a - 1)}{2 \cdot (a + 1)}\]

\[\boxed{\text{268.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

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

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

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

\[= \frac{5a^{2} - 10a + 5}{2 \cdot (a - 1)(a + 1)} =\]

\[= \frac{5 \cdot \left( a^{2} - 2a + 1 \right)}{2 \cdot (a - 1)(a + 1)} =\]

\[= \frac{5(a - 1)^{2}}{2 \cdot (a - 1)(a + 1)} =\]

\[= \frac{5 \cdot (a - 1)}{2 \cdot (a + 1)}\]