2. Упростите выражение: 1) \(\frac{2a}{a-2}+\frac{a+7}{8-4a}\cdot\frac{32}{7a+a^2}\); 2) \(\left(\frac{a-1}{a+1}-\frac{a+1}{a-1}\right):\frac{2a}{1-a^2}\).

1. \[\frac{2a}{a-2}+\frac{a+7}{8-4a}\cdot\frac{32}{7a+a^2}=\frac{2a}{a-2}+\frac{a+7}{-4(a-2)}\cdot\frac{32}{a(a+7)}=\frac{2a}{a-2}-\frac{8}{a(a-2)}=\frac{2a^2-8}{a(a-2)}=\frac{2(a-2)(a+2)}{a(a-2)}=\frac{2(a+2)}a.\]
2. \[\left(\frac{a-1}{a+1}-\frac{a+1}{a-1}\right):\frac{2a}{1-a^2}=\frac{(a-1)^2-(a+1)^2}{a^2-1}\cdot\frac{1-a^2}{2a}=\frac{-4a}{a^2-1}\cdot\frac{-(a^2-1)}{2a}=2.\]

Ответ: 1) \(\frac{2(a+2)}a\); 2) \(2\).