Для каждого значения а решите уравнение: (a^2+2a-8)x=a^2-4.

\[\left( a^{2} + 2a - 8 \right)x = a² - 4\]

\[x = \frac{a^{2} - 4}{a^{2} + 2a - 8} =\]

\[a^{2} + 2a - 8 = 0\]

\[a_{1} + a_{2} = - 2;\ \ a_{1} \cdot a_{2} = - 8\]

\[a_{1} = - 4;\ \ \ \ \ \ \ \ \ \ \ \ a_{2} = 2\]

\[a^{2} + 2a - 8 = (a + 4)(a - 2).\]

\[1)\ \ a = 2:\]

\[\left( 2^{2} + 2 \cdot 2 - 8 \right)x = 2^{2} - 4\]

\[0 \cdot x = 0 \Longrightarrow x - любое.\]

\[2)\ \ a = - 4:\]

\[нет\ решения.\]

\[3)\ \ a = - 2:\]

\[x = 0.\]

\[4)\ \ a \neq 2,\ a \neq - 4,\ a \neq - 2:\]

\[x = \frac{a + 2}{a + 4}.\]