Вычислите алгебраические дроби:

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ФИО:Телефон:Емаил:Полное описание сути нарушения прав (почему распространение данной информации запрещено Правообладателем):

Accepted Answer

$$\frac{3}{x-y} - \frac{x-2}{y-x} = \frac{3}{x-y} + \frac{x-2}{x-y} = \frac{3+x-2}{x-y} = \frac{x+1}{x-y}$$
$$\frac{2x}{x-y} - \frac{8x+4y}{2x-2y} = \frac{2x}{x-y} - \frac{8x+4y}{2(x-y)} = \frac{4x - (8x+4y)}{2(x-y)} = \frac{4x - 8x - 4y}{2(x-y)} = \frac{-4x-4y}{2(x-y)} = \frac{-4(x+y)}{2(x-y)} = \frac{-2(x+y)}{x-y}$$
$$\frac{3}{x-y} - \frac{2x+3y}{(y-x)^2} = \frac{3}{x-y} - \frac{2x+3y}{(x-y)^2} = \frac{3(x-y) - (2x+3y)}{(x-y)^2} = \frac{3x - 3y - 2x - 3y}{(x-y)^2} = \frac{x - 6y}{(x-y)^2}$$
$$\frac{x}{x-y} - \frac{xy}{x^2-y^2} = \frac{x}{x-y} - \frac{xy}{(x-y)(x+y)} = \frac{x(x+y) - xy}{(x-y)(x+y)} = \frac{x^2+xy - xy}{(x-y)(x+y)} = \frac{x^2}{(x-y)(x+y)} = \frac{x^2}{x^2-y^2}$$
$$\frac{3y}{x-y} - \frac{y}{x} = \frac{3yx - y(x-y)}{x(x-y)} = \frac{3yx - yx + y^2}{x(x-y)} = \frac{2yx + y^2}{x(x-y)} = \frac{y(2x+y)}{x(x-y)}$$
$$\frac{-2xy}{x-y} - x + y = \frac{-2xy - (x-y)x + (x-y)y}{x-y} = \frac{-2xy - x^2 + xy + xy - y^2}{x-y} = \frac{-x^2 - y^2}{x-y} = -\frac{x^2+y^2}{x-y}$$
$$(xy-y^2) : \frac{x^2-y^2}{y} = \frac{y(x-y)}{1} \cdot \frac{y}{(x-y)(x+y)} = \frac{y^2}{x+y}$$
$$\frac{2x+3y^2}{y} \cdot \frac{y^3-xy^2}{2xy+3y^3} = \frac{(2x+3y^2) \cdot y^2(y-x)}{y \cdot y(2x+3y^2)} = \frac{y(y-x)}{y} = y-x$$