Упростите выражение 3a/(a-4)-(a+2)/(2a-8)*96/(a^2+2a).

Ответ:

\[\frac{3a}{a - 4} - \frac{a + 2}{2a - 8} \cdot \frac{96}{a^{2} + 2a} =\]

\[= \frac{3a}{a - 4} - \frac{(a + 2) \cdot 96}{2(a - 4) \cdot a(a + 2)} =\]

\[= \frac{3a^{\backslash a}}{a - 4} - \frac{48}{a(a - 4)} = \frac{3a^{2} - 48}{a(a - 4)} =\]

\[= \frac{3\left( a^{2} - 16 \right)}{a(a - 4)} = \frac{3(a - 4)(a + 4)}{a(a - 4)} = \frac{3a + 12}{a}\]