7)

[tex] x\neq - 0.5 \: \: \: and \: \: \: x\neq0.5 \\ \frac{2x - 1}{2x + 1} = \frac{2x + 1}{2x - 1} + \frac{4}{1 - 4 {x}^{2} } \\ \frac{2x - 1}{2x + 1} - \frac{2x + 1}{2x - 1} + \frac{4}{(2x - 1)(2x + 1)} = 0 \\ \frac{(2x - 1) {}^{2} - (2x + 1) {}^{2} + 4 }{(2x - 1)(2x + 1)} = 0 \\ 4 {x}^{2} - 4x + 1 - (4 {x}^{2} + 4x + 1) + 4 = 0 \\ 4 {x}^{2} - 4x + 5 - 4 {x}^{2} - 4x - 1 = 0 \\ - 8x + 4 = 0 \\ 8x = 4 \\ x = 4 \div 8 \\ x = 0.5[/tex]

Не подходит

Ответ: нет решений

8)

[tex] x\neq0 \: \: \:and \: \: \: x\neq - 1 \: \: \: and \: \: \: x\neq1\\ \frac{6}{ {x}^{2} + x } - \frac{x - 6}{ {x}^{2} - x} + \frac{10}{ {x}^{2} - 1 } = 0 \\ \frac{6}{x(x + 1)} - \frac{x - 6}{x(x - 1)} + \frac{10}{(x - 1)(x + 1)} = 0 \\ \frac{6(x - 1) - (x - 6)(x + 1) + 10x}{x(x - 1)(x + 1)} = 0 \\ \frac{6x - 6 - ( {x}^{2} + x - 6x - 6) + 10x}{x(x - 1)(x + 1)} = 0 \\ 6x - 6 - {x}^{2} + 5x + 6 + 10x = 0 \\ - {x}^{2} + 21x = 0 \\ {x}^{2} - 21x = 0 \\ x(x - 21) = 0 \\ x_{1} = 0\\ x_{2} = 21[/tex]

Первый корень не подходит

Ответ: х = 21