Упростите выражение: (8x/(x-2)+2x)∶(4x+8)/(7x-14).

Ответ:

\[\left( \frac{8x}{x - 2} + 2x^{\backslash x - 2} \right)\ :\frac{4x + 8}{7x - 14} =\]

\[= \frac{8x + 2x(x - 2)}{x - 2}\ :\frac{4 \cdot (x + 2)}{7 \cdot (x - 2)} =\]

\[= \frac{\left( 8x + 2x^{2} - 4x \right) \cdot 7 \cdot (x - 2)}{(x - 2) \cdot 4 \cdot (x + 2)} =\]

\[= \frac{\left( 4x + 2x^{2} \right) \cdot 7}{4 \cdot (x + 2)} =\]

\[= \frac{2x(x + 2) \cdot 7}{4 \cdot (x + 2)} = \frac{7x}{2}\]