Найдите значение выражения (a-2)/(a^2+4)*((a+2)/(a-2)+(a-2)/(a+2)) при a=-2,5.

Ответ:

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

\[= \frac{a - 2}{a^{2} + 4} \cdot \frac{a^{2} + 4a + 4 + a^{2} - 4a + 4}{(a - 2)(a + 2)} =\]

\[= \frac{1}{a^{2} + 4} \cdot \frac{2a^{2} + 8}{a + 2} = \frac{2 \cdot \left( a^{2} + 4 \right)}{\left( a^{2} + 4 \right)(a + 2)} =\]

\[= \frac{2}{a + 2}\]

\[a = - 2,5:\]

\[\frac{2}{- 2,5 + 2} = \frac{2}{- 0,5} = - \frac{20}{5} = - 4.\]

\[Ответ:\ - 4.\]