6. 7 1) (x/(x+y) + x^2/(y^2-x^2)) : (x^2/(x+y) - x^3/(x^2+y^2+2xy));

1) $$(\frac{x}{x+y} + \frac{x^2}{y^2-x^2}) : (\frac{x^2}{x+y} - \frac{x^3}{x^2+y^2+2xy}) = (\frac{x}{x+y} + \frac{x^2}{(y-x)(y+x)}) : (\frac{x^2}{x+y} - \frac{x^3}{(x+y)^2}) = \frac{x(y-x) + x^2}{(x+y)(y-x)} : \frac{x^2(x+y) - x^3}{(x+y)^2} = \frac{xy - x^2 + x^2}{(x+y)(y-x)} : \frac{x^3 + x^2y - x^3}{(x+y)^2} = \frac{xy}{(x+y)(y-x)} : \frac{x^2y}{(x+y)^2} = \frac{xy}{(x+y)(y-x)} \cdot \frac{(x+y)^2}{x^2y} = \frac{xy(x+y)(x+y)}{(x+y)(y-x)x^2y} = \frac{x+y}{x(y-x)} = \frac{x+y}{-x(x-y)} = -\frac{x+y}{x(x-y)}$$.

Ответ: $$- \frac{x+y}{x(x-y)}$$