Упростите выражение:
а) $\frac{x^2 - 2x}{x - 3} - \frac{4x - 9}{x - 3}$;
б) $\frac{y^2 - 10}{y - 8} - \frac{54}{y - 8}$;
в) $\frac{a^2}{a^2 - b^2} + \frac{b^2}{b^2 - a^2}$;
г) $\frac{x^2 - 2x}{x^2 - y^2} - \frac{2y - y^2}{y^2 - x^2}$.
$\frac{x^2 - 2x}{x - 3} - \frac{4x - 9}{x - 3} = \frac{x^2 - 2x - (4x - 9)}{x - 3} = \frac{x^2 - 6x + 9}{x - 3} = \frac{(x - 3)^2}{x - 3} = x - 3$
$\frac{y^2 - 10}{y - 8} - \frac{54}{y - 8} = \frac{y^2 - 10 - 54}{y - 8} = \frac{y^2 - 64}{y - 8} = \frac{(y - 8)(y + 8)}{y - 8} = y + 8$
$\frac{a^2}{a^2 - b^2} + \frac{b^2}{b^2 - a^2} = \frac{a^2}{a^2 - b^2} - \frac{b^2}{a^2 - b^2} = \frac{a^2 - b^2}{a^2 - b^2} = 1$
$\frac{x^2 - 2x}{x^2 - y^2} - \frac{2y - y^2}{y^2 - x^2} = \frac{x^2 - 2x}{x^2 - y^2} + \frac{2y - y^2}{x^2 - y^2} = \frac{x^2 - 2x + 2y - y^2}{x^2 - y^2} = \frac{(x - y)(x + y) - 2(x - y)}{(x - y)(x + y)} = \frac{(x - y)(x + y - 2)}{(x - y)(x + y)} = \frac{x + y - 2}{x + y}$
Пожауйста, оцените решение
