8) $$\frac{2x}{3y} : \frac{x^4}{y^2} =$$ 9) $$\frac{a}{b-1} \cdot \frac{b-1}{2} =$$ 10) $$\frac{3x}{a-2} \cdot \frac{(2-a)}{9} =$$ 11) $$\frac{a}{2} + \frac{a-6}{3} =$$ 12) $$\frac{3}{x(x+5)} \cdot \frac{2(x+5)}{x} =$$ 13) $$\frac{2}{a-2} + \frac{2}{a} =$$ 14) $$\frac{6y+1}{2x} \cdot \frac{1}{x} =$$ 15) $$\frac{b+2}{b^2-9} - \frac{b}{9-b^2} =$$ 16) $$\frac{1}{n-1} + \frac{m}{1-m} =$$ 17) $$\frac{a^2}{a+3} \cdot \frac{2}{a+3} =$$ 18) $$\frac{(a+3)^2}{2x^2} - \frac{x}{(a+3)} =$$ 19) $$\frac{n^2}{9a} + \frac{n^2}{3a} =$$ 20) $$\frac{a+3}{a-1} \cdot \frac{7-a}{a+3} =$$

Решим каждое уравнение по порядку: 8) $$ \frac{2x}{3y} : \frac{x^4}{y^2} = \frac{2x}{3y} \cdot \frac{y^2}{x^4} = \frac{2xy^2}{3yx^4} = \frac{2y}{3x^3} $$ 9) $$ \frac{a}{b-1} \cdot \frac{b-1}{2} = \frac{a(b-1)}{2(b-1)} = \frac{a}{2} $$ 10) $$ \frac{3x}{a-2} \cdot \frac{(2-a)}{9} = \frac{3x(2-a)}{9(a-2)} = \frac{3x \cdot (-1)(a-2)}{9(a-2)} = -\frac{3x}{9} = -\frac{x}{3} $$ 11) $$ \frac{a}{2} + \frac{a-6}{3} = \frac{3a + 2(a-6)}{6} = \frac{3a + 2a - 12}{6} = \frac{5a - 12}{6} $$ 12) $$ \frac{3}{x(x+5)} \cdot \frac{2(x+5)}{x} = \frac{3 \cdot 2(x+5)}{x(x+5) \cdot x} = \frac{6(x+5)}{x^2(x+5)} = \frac{6}{x^2} $$ 13) $$ \frac{2}{a-2} + \frac{2}{a} = \frac{2a + 2(a-2)}{a(a-2)} = \frac{2a + 2a - 4}{a(a-2)} = \frac{4a - 4}{a(a-2)} = \frac{4(a-1)}{a(a-2)} $$ 14) $$ \frac{6y+1}{2x} \cdot \frac{1}{x} = \frac{6y+1}{2x^2} $$ 15) $$ \frac{b+2}{b^2-9} - \frac{b}{9-b^2} = \frac{b+2}{b^2-9} + \frac{b}{b^2-9} = \frac{b+2+b}{b^2-9} = \frac{2b+2}{b^2-9} = \frac{2(b+1)}{(b-3)(b+3)} $$ 16) $$ \frac{1}{n-1} + \frac{m}{1-m} = \frac{1}{n-1} - \frac{m}{m-1} = \frac{1 - m(n-1)}{(n-1)(1-m)} = \frac{1 - mn + m}{(n-1)(1-m)} $$ 17) $$ \frac{a^2}{a+3} \cdot \frac{2}{a+3} = \frac{2a^2}{(a+3)^2} $$ 18) $$ \frac{(a+3)^2}{2x^2} - \frac{x}{(a+3)} = \frac{(a+3)^3 - 2x^3}{2x^2(a+3)} $$ 19) $$ \frac{n^2}{9a} + \frac{n^2}{3a} = \frac{n^2 + 3n^2}{9a} = \frac{4n^2}{9a} $$ 20) $$ \frac{a+3}{a-1} \cdot \frac{7-a}{a+3} = \frac{(a+3)(7-a)}{(a-1)(a+3)} = \frac{7-a}{a-1} $$