Решение уравнений

1. $$\frac{2}{9}x = -5\frac{5}{9}$$

   $$\frac{2}{9}x = -\frac{50}{9}$$

   $$x = -\frac{50}{9} \cdot \frac{9}{2}$$

   $$\mathbf{x = -25}$$

2. $$\frac{1}{2x+5}=\frac{1}{3x-8}$$

   $$2x + 5 = 3x - 8$$

   $$3x - 2x = 5 + 8$$

   $$\mathbf{x = 13}$$

3. $$\frac{1}{5x-8}=\frac{1}{3x+21}$$

   $$5x - 8 = 3x + 21$$

   $$5x - 3x = 21 + 8$$

   $$2x = 29$$

   $$\mathbf{x = 14.5}$$

4. $$\frac{1}{(6x-13)^2} = \frac{1}{(6x-11)^2}$$

   $$(6x-13)^2 = (6x-11)^2$$

   $$36x^2 - 156x + 169 = 36x^2 - 132x + 121$$

   $$36x^2 - 36x^2 - 156x + 132x = 121 - 169$$

   $$-24x = -48$$

   $$\mathbf{x = 2}$$

5. $$(x+9)^2 = 36x$$

   $$x^2 + 18x + 81 = 36x$$

   $$x^2 - 18x + 81 = 0$$

   $$(x - 9)^2 = 0$$

   $$\mathbf{x = 9}$$