Решебник по алгебре 8 класс Мерзляк ФГОС Задание 166

\[\boxed{\text{166\ (166).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\frac{a^{2} - 36}{a^{2} + ab - 6a - 6b}\ :\]

\[:\frac{a^{2} + ab + 6a + 6b}{a^{2} + 2ab + b^{2}} =\]

\[= \frac{(a - 6)(a + 6)(a + b)^{2}}{\left( a^{2} + ab - 6a - 6b \right)\left( a^{2} + ab + 6a + 6b \right)} =\]

\[= \frac{(a - 6)(a + 6)(a + b)^{2}}{\left( a(a + b) - 6(a + b) \right)\left( a(a + b) + 6(a + b) \right)} =\]

\[= \frac{(a - 6)(a + 6)(a + b)^{2}}{(a + b)(a - 6)(a + b)(a + 6)} =\]

\[= 1\]

\[2)\ \frac{a^{2} + a - ab - b}{a^{2} + a + ab + b}\ :\]

\[:\frac{a^{2} - a - ab + b}{a^{2} - a + ab - b} =\]

\[= \frac{\left( a(a + 1) - b(a + 1) \right)\left( a(a - 1) + b(a - 1) \right)}{\left( a(a + 1) + b(a + 1) \right)\left( a(a - 1) - b(a - 1) \right)} =\]

\[= \frac{(a + 1)(a - b)(a - 1)(a + b)}{(a + 1)(a + b)(a - 1)(a - b)} =\]

\[= 1\]

\[\boxed{\text{166.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\frac{8a^{2}}{a - 3b}\ :\frac{6a^{3}}{a^{2} - 9b^{2}} \cdot\]

\[\cdot \frac{3a}{4a + 12b} = 1\]

\[Упростим\ левую\ часть\ \]

\[тождества:\]

\[\frac{8a^{2}(a - 3b)(a + 3b) \cdot 3a}{(a - 3b) \cdot 6a^{3} \cdot 4(a + 3b)} = 1\]

\[\frac{2a^{2}}{2a^{2}} = 1\]

\[1 = 1.\]

\[Что\ и\ требовалось\ доказать.\]