Question

6.49
Выполнить действия ​

Answer 1

Ответ:

1

$\frac{1}{2a -b } - \frac{1}{2 a+ b} = \frac{2a + b - (2a - b)}{(2 a-b )(2a + b)} = \\ = \frac{2a + b - 2a + b}{(2a - b)(2a + b)} = \frac{2b}{4 {a}^{2} - b {}^{2} }$

2

$\frac{1}{3m - n} + \frac{1}{3m + n} = \frac{3m + n + 3m - n}{(3m - n)(3m + n)} = \\ = \frac{6m}{9 {m}^{2} - n {}^{2} }$

3

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

4

$\frac{4}{p + q} + \frac{2}{p - q} = \frac{4(p - q) + 2(p + q)}{(p - q)(p + q)} = \\ = \frac{4p - 4q + 2p + 2q}{ {p}^{2} - q {}^{2} } = \frac{6p - 2q}{p {}^{2} - q {}^{2} }$