Задание 3. Упростите выражение:

• а) $$ \frac{x+1}{x+y} + \frac{y+1}{x+y} - \frac{y-x}{x+y} = \frac{x+1+y+1-y+x}{x+y} = \frac{2x+2}{x+y} = \frac{2(x+1)}{x+y} $$
• б) $$ \frac{3}{a-4} - \frac{a+2}{2a-8} \cdot \frac{96}{a^2+2a} = \frac{3}{a-4} - \frac{a+2}{2(a-4)} \cdot \frac{96}{a(a+2)} = \frac{3}{a-4} - \frac{48}{a(a-4)} = \frac{3a-48}{a(a-4)} = \frac{3(a-16)}{a(a-4)} $$
• в) $$ (\frac{a+7}{a-7} - \frac{a-7}{a+7}) \cdot \frac{14a}{49-a^2} = (\frac{(a+7)^2 - (a-7)^2}{(a-7)(a+7)}) \cdot \frac{14a}{49-a^2} = \frac{a^2+14a+49-a^2+14a-49}{(a-7)(a+7)} \cdot \frac{14a}{49-a^2} = \frac{28a}{(a-7)(a+7)} \cdot \frac{14a}{49-a^2} = \frac{28a \cdot 14a}{(a-7)(a+7)(49-a^2)} = \frac{392a^2}{-(a-7)(a+7)(a-7)(a+7)} = -\frac{392a^2}{(a-7)^2(a+7)^2} $$