Упростите выражение:
1) $\frac{4x - y}{x^2 - y^2} + \frac{1}{x - y}$;
2) $\frac{y^2}{y^2 - 81} - \frac{y}{y + 9}$;
3) $\frac{10a}{25a^2 - 9} - \frac{1}{5a + 3}$;
4) $\frac{n}{n - 7} - \frac{n^2}{n^2 - 14n + 49}$.
$\frac{4x - y}{x^2 - y^2} + \frac{1}{x - y} = \frac{4x - y}{(x - y)(x + y)} + \frac{1}{x - y} = \frac{4x - y + x + y}{(x - y)(x + y)} = \frac{5x}{x^2 - y^2}$
$\frac{y^2}{y^2 - 81} - \frac{y}{y + 9} = \frac{y^2}{(y - 9)(y + 9)} - \frac{y}{y + 9} = \frac{y^2 - y(y - 9)}{(y - 9)(y + 9)} = \frac{y^2 - y^2 + 9y}{y^2 - 81} = \frac{9y}{y^2 - 81}$
$\frac{10a}{25a^2 - 9} - \frac{1}{5a + 3} = \frac{10a}{(5a - 3)(5a + 3)} - \frac{1}{5a + 3} = \frac{10a - (5a - 3)}{(5a - 3)(5a + 3)} = \frac{10a - 5a + 3}{(5a - 3)(5a + 3)} = \frac{5a + 3}{(5a - 3)(5a + 3)} = \frac{1}{5a - 3}$
$\frac{n}{n - 7} - \frac{n^2}{n^2 - 14n + 49} = \frac{n}{n - 7} - \frac{n^2}{(n - 7)^2} = \frac{n(n - 7) - n^2}{(n - 7)^2} = \frac{n^2 - 7n - n^2}{(n - 7)^2} = \frac{-7n}{(n - 7)^2} = -\frac{7n}{(n - 7)^2}$
Пожауйста, оцените решение
