Упростите выражение: (2x/(x-2)-1/(x+2)):(6x^2+9x+6)/(x^2-4).

Ответ:

\[\left( \frac{2x^{\backslash x + 2}}{x - 2} - \frac{1^{\backslash x - 2}}{x + 2} \right)\ :\frac{6x^{2} + 9x + 6}{x^{2} - 4} =\]

\[= \frac{2x^{2} + 4x - x + 2}{(x - 2)(x + 2)} \cdot \frac{x^{2} - 4}{6x^{2} + 9x + 6} =\]

\[= \frac{\left( 2x^{2} + 3x + 2 \right)\left( x^{2} - 4 \right)}{\left( x^{2} - 4 \right) \cdot 3\left( 2x^{2} + 3x + 2 \right)} = \frac{1}{3}.\]