1. 4 1) (1/x+2x)⋅x³/4; 3) (2a/1+a-1/a):a/1+a; 4 1) b²/(2b-a)⋅(2-a/b); 3) (5+3x)/x⁶:(3/5+1/x); 5 1) (3-(x+y)/(x-y)):(3x/(x+y)-2); 2) (9a-3b)/(a+b)-1:(3+(a+b)/(a-b)).

Ответ: Решения уравнений представлены ниже.

1. 1) \(\left(\frac{1}{x} + 2x\right) \cdot \frac{x^3}{4}\)
   \(\frac{1}{x} \cdot \frac{x^3}{4} + 2x \cdot \frac{x^3}{4} = \frac{x^2}{4} + \frac{x^4}{2} = \frac{x^2 + 2x^4}{4} = \frac{x^2(1 + 2x^2)}{4}\)
2. 3) \(\left(\frac{2a}{1+a} - \frac{1}{a}\right) : \frac{a}{1+a}\)
   \(\frac{2a^2 - (1+a)}{a(1+a)} : \frac{a}{1+a} = \frac{2a^2 - 1 - a}{a(1+a)} \cdot \frac{1+a}{a} = \frac{2a^2 - a - 1}{a^2}\)
3. 1) \(\frac{b^2}{2b-a} \cdot \left(2 - \frac{a}{b}\right)\)
   \(\frac{b^2}{2b-a} \cdot \frac{2b-a}{b} = b\)
4. 3) \(\frac{5+3x}{x^6} : \left(\frac{3}{5} + \frac{1}{x}\right)\)
   \(\frac{5+3x}{x^6} : \frac{3x+5}{5x} = \frac{5+3x}{x^6} \cdot \frac{5x}{3x+5} = \frac{5}{x^5}\)
5. 1) \(\left(3 - \frac{x+y}{x-y}\right) : \left(\frac{3x}{x+y} - 2\right)\)
   \(\frac{3(x-y) - (x+y)}{x-y} : \frac{3x - 2(x+y)}{x+y} = \frac{3x - 3y - x - y}{x-y} : \frac{3x - 2x - 2y}{x+y} = \frac{2x - 4y}{x-y} : \frac{x - 2y}{x+y} = \frac{2(x - 2y)}{x-y} \cdot \frac{x+y}{x - 2y} = \frac{2(x+y)}{x-y}\)
6. 2) \(\left(\frac{9a-3b}{a+b} - 1\right) : \left(3 + \frac{a+b}{a-b}\right)\)
   \(\frac{9a-3b - (a+b)}{a+b} : \frac{3(a-b) + (a+b)}{a-b} = \frac{8a - 4b}{a+b} : \frac{3a - 3b + a + b}{a-b} = \frac{4(2a - b)}{a+b} : \frac{4a - 2b}{a-b} = \frac{4(2a - b)}{a+b} \cdot \frac{a-b}{2(2a - b)} = \frac{2(a-b)}{a+b}\)

Ответ: Решения уравнений представлены выше.