04.23. a) x + y = x²+ y²; x-y б) х-у- х²+ y²

a) $$x+y - \frac{x^2+y^2}{x-y} = \frac{(x+y)(x-y) - (x^2+y^2)}{x-y} = \frac{x^2 - y^2 - x^2 - y^2}{x-y} = \frac{-2y^2}{x-y} = \frac{2y^2}{y-x}$$ б) $$x-y - \frac{x^2+y^2}{x-y} = \frac{(x-y)(x-y) - (x^2+y^2)}{x-y} = \frac{x^2 - 2xy + y^2 - x^2 - y^2}{x-y} = \frac{-2xy}{x-y} = \frac{2xy}{y-x}$$ Ответ: a) $$\frac{2y^2}{y-x}$$; б) $$\frac{2xy}{y-x}$$