Найдите значение выражения (x-3)/(x^2+9)*((x+3)/(x-3)+(x-3)/(x+3)) при x=-3,4.

Ответ:

\[\frac{x - 3}{x^{2} + 9} \cdot \left( \frac{x + 3^{\backslash x + 3}}{x - 3} + \frac{x - 3^{\backslash x - 3}}{x + 3} \right) =\]

\[= \frac{x - 3}{x^{2} + 9} \cdot \frac{x^{2} + 6x + 9 + x^{2} - 6x + 9}{(x - 3)(x + 3)} =\]

\[= \frac{1}{x^{2} + 9} \cdot \frac{2x^{2} + 18}{x + 3} = \frac{2 \cdot (x^{2} + 9)}{(x^{2} + 9)(x + 3)} =\]

\[= \frac{2}{x + 3}\]

\[x = - 3,4:\]

\[\frac{2}{- 3,4 + 3} = \frac{2}{- 0,4} = - \frac{20}{4} = - 5.\]

\[Ответ:\ - 5.\]