Решение:

1. а) $$ \frac{-4x+9y}{4} + \frac{4x-7y}{4} = \frac{-4x+9y+4x-7y}{4} = \frac{2y}{4} = \frac{y}{2} $$

   Ответ: $$ \frac{y}{2} $$

2. б) $$ \frac{9x-8y}{8} - \frac{9x+4y}{8} = \frac{9x-8y-(9x+4y)}{8} = \frac{9x-8y-9x-4y}{8} = \frac{-12y}{8} = -\frac{3y}{2} $$

   Ответ: $$ -\frac{3y}{2} $$

3. в) $$ \frac{81t^2}{18t+4x} - \frac{4x^2}{18t+4x} = \frac{81t^2 - 4x^2}{18t+4x} = \frac{(9t-2x)(9t+2x)}{2(9t+2x)} = \frac{9t-2x}{2} $$

   Ответ: $$ \frac{9t-2x}{2} $$

4. г) $$ \frac{a^2}{5a+15b^2} - \frac{9b^4}{5a+15b^2} = \frac{a^2 - 9b^4}{5a+15b^2} = \frac{(a-3b^2)(a+3b^2)}{5(a+3b^2)} = \frac{a-3b^2}{5} $$

   Ответ: $$ \frac{a-3b^2}{5} $$

5. д) $$ \frac{-5d+7c}{6} + \frac{5d+c}{6} = \frac{-5d+7c+5d+c}{6} = \frac{8c}{6} = \frac{4c}{3} $$

   Ответ: $$ \frac{4c}{3} $$

6. е) $$ \frac{36-c^2}{c+6} = \frac{(6-c)(6+c)}{c+6} = 6-c $$

   Ответ: $$ 6-c $$