Question

$\frac{2 }{ \times - y \\ \\ } - \frac{2}{ \times + y}$
$\frac{2 \times }{ \times - 4 } - \frac{5 \times - 12}{ { \times }^{2} - 16}$
$\frac{1}{a + b \\ } - \frac{1}{a - b}$
ПОЖАЛУЙСТА РЕШИТЕ Я ДАМ 100 БАЛЛОВ
​

Answer 1

1)

$\frac{2}{x - y} - \frac{2}{x + y} = \frac{2(x + y) - 2(x - y)}{(x - y)(x + y)} = \\ \frac{2x + 2y - 2x +2 y}{ {x}^{2} - {y}^{2} } = \frac{4y}{ {x}^{2} - {y}^{2} }$

2)

$\frac{2x}{x - 4} - \frac{5x - 12}{ {x}^{2} - 16} = \frac{2x }{x - 4} - \frac{5x - 12}{(x - 4)(x + 4) } = \\ \frac{2x(x + 4) - (5x - 12)}{(x - 4)(x + 4)} = \frac{2 {x}^{2} + 8x - 5x + 12 }{(x - 4)(x + 4)} = \\ \frac{2 {x}^{2} + 3x + 12 }{ {x}^{2} - 16 }$

3)

$\frac{1}{a + b} - \frac{1}{a - b} = \frac{a - b - (a + b)}{(a - b)(a + b)} = \\ \frac{a - b - a - b}{ {a}^{2} - {b}^{2} } = - \frac{2b}{ {a}^{2} - {b}^{2} }$