ГДЗ по алгебре 9 класс Макарычев ФГОС Задание 232

\[\boxed{\text{233.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[\textbf{а)}\ \frac{a^{3} - 9a}{a^{2} + a - 12} = \frac{a\left( a^{2} - 9 \right)}{a^{2} + a - 12} =\]

\[= \frac{a(a - 3)(a + 3)}{a^{2} + a - 12};\]

\[\frac{a(a - 3)(a + 3)}{a^{2} + a - 12} = 0;\]

\[a_{1} = 0,\ \ a_{2} = 3,\ \ a_{3} = - 3.\]

\[ОДЗ:\ a^{2} + a - 12 \neq 0\]

\[D = 1 + 4 \cdot 12 = 49\]

\[a = \frac{- 1 \pm 7}{2} = - 4;3\]

\[\Longrightarrow a \neq - 4,\ \ a \neq - 3.\]

\[Дробь\ превращается\ в\ ноль\ \]

\[при\ \ a_{1} = 0,\ a_{2} = 3.\]

\[\textbf{б)}\ \frac{a^{5} + 2a^{4}}{a^{3} + a + 10} = \frac{a^{4} \cdot (a + 2)}{a^{3} + a + 10};\]

\[\frac{a^{4} \cdot (a + 2)}{a^{3} + a + 10} = 0\]

\[a_{1} = 0,\ \ a_{2} = - 2.\]

\[ОДЗ:a^{3} + a + 10 =\]

\[= (a + 10)\left( a^{2} - 2a + 5 \right) \neq 0 \Longrightarrow\]

\[\Longrightarrow a \neq - 2.\]

\[Дробь\ превращается\ в\ ноль\ \]

\[при\ a = 0.\]

\[\textbf{в)}\ \frac{a^{5} - 4a^{4} + 4a^{3}}{a^{4} - 16} =\]

\[= \frac{a^{3}\left( a^{2} - 4a + 4 \right)}{\left( a^{2} - 4 \right)\left( a^{2} + 4 \right)} =\]

\[= \frac{a^{3}(a - 2)^{2}}{(a - 2)(a + 2)\left( a^{2} + 4 \right)} =\]

\[= \frac{a^{3}(a - 2)}{(a + 2)\left( a^{2} + 4 \right)};\]

\[\frac{a^{3}(a - 2)}{(a + 2)\left( a^{2} + 4 \right)} = 0\ \ при\ \]

\[\ a_{1} = 0\ \ или\ \ a_{2} = 2;\]

\[ОДЗ:\ a + 2 \neq 0,\ \ a \neq - 2.\]

\[Дробь\ превращается\ в\ ноль\ \]

\[при\ \ a = 0.\ \]