109. Упростите выражение: 1) (4x - y)/(x^2 - y^2) + 1/(x - y); 2) y^2/(y^2 - 81) - y/(y + 9); 3) 10a/(25a^2 - 9) - 1/(5a + 3); 4) n/(n - 7) - n^2/(n^2 - 14n + 49).

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109. Упростите выражение: 1) (4x - y)/(x^2 - y^2) + 1/(x - y); 2) y^2/(y^2 - 81) - y/(y + 9); 3) 10a/(25a^2 - 9) - 1/(5a + 3); 4) n/(n - 7) - n^2/(n^2 - 14n + 49).

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1) $\frac{4x - y}{x^2 - y^2} + \frac{1}{x - y} = \frac{4x - y}{(x - y)(x + y)} + \frac{x + y}{(x - y)(x + y)} = \frac{4x - y + x + y}{(x - y)(x + y)} = \frac{5x}{(x - y)(x + y)} = \frac{5x}{x^2 - y^2}$ 2) $\frac{y^2}{y^2 - 81} - \frac{y}{y + 9} = \frac{y^2}{(y - 9)(y + 9)} - \frac{y(y - 9)}{(y - 9)(y + 9)} = \frac{y^2 - y^2 + 9y}{(y - 9)(y + 9)} = \frac{9y}{y^2 - 81}$ 3) $\frac{10a}{25a^2 - 9} - \frac{1}{5a + 3} = \frac{10a}{(5a - 3)(5a + 3)} - \frac{5a - 3}{(5a - 3)(5a + 3)} = \frac{10a - 5a + 3}{(5a - 3)(5a + 3)} = \frac{5a + 3}{(5a - 3)(5a + 3)} = \frac{1}{5a - 3}$ 4) $\frac{n}{n - 7} - \frac{n^2}{n^2 - 14n + 49} = \frac{n}{n - 7} - \frac{n^2}{(n - 7)^2} = \frac{n(n - 7)}{(n - 7)^2} - \frac{n^2}{(n - 7)^2} = \frac{n^2 - 7n - n^2}{(n - 7)^2} = \frac{-7n}{(n - 7)^2}$

109. Упростите выражение: 1) (4x - y)/(x^2 - y^2) + 1/(x - y); 2) y^2/(y^2 - 81) - y/(y + 9); 3) 10a/(25a^2 - 9) - 1/(5a + 3); 4) n/(n - 7) - n^2/(n^2 - 14n + 49).

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