Упростите выражение: 2a/(a-2)+(a+7)/(8-4a)*32/(7a+a^2).

Ответ:

\[\frac{2a}{a - 2} + \frac{a + 7}{8 - 4a} \cdot \frac{32}{7a + a^{2}} =\]

\[= \frac{2a}{a - 2} + \frac{32(a + 7)}{4(2 - a)a(7 + a)} =\]

\[= \frac{2a^{\backslash a}}{a - 2} + \frac{8}{a(2 - a)} = \frac{2a^{2} - 8}{a(a - 2)} =\]

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

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