Verified answer

4.

[tex]1 + 2x\neq0 \\ 2x\neq - 1 \\ x\neq - 0.5 \\ \frac{4x + 2}{1 + 2x} = \frac{6x + 5}{1} \\ (6x + 5)(1 + 2x) = 4x + 2 \\ 6x + 12 {x}^{2} + 5 + 10x - 4x - 2 = 0 \\ 12 {x}^{2} + 12x + 3 = 0 \\ 4 {x}^{2} + 4x + 1 = 0 \\ (2x) {}^{2} + 2 \times 2x \times 1 + {1}^{2} = 0 \\ (2x + 1) {}^{2} = 0 \\ 2x + 1 = 0 \\ 2x = - 1 \\ x = - 1 \div 2 \\ x = - 0.5[/tex]

Корень не подходит

Ответ: нет корней

5.

[tex]x\neq5 \: \: \: \: \: and \: \: \: \: x\neq - 5 \\ \frac{4}{x - 5} - \frac{2}{x + 5} = \frac{ {x}^{2} + 15 }{ {x}^{2} - 25} \\ \frac{4}{x - 5} - \frac{2}{x + 5} - \frac{ {x}^{2} + 15 }{(x - 5)(x + 5)} = 0 \\ \frac{4(x + 5) - 2(x - 5) - (x {}^{2} + 15)}{(x - 5)(x + 5)} = 0 \\ 4x + 20 - 2x + 10 - {x}^{2} - 15 = 0 \\ - {x}^{2} + 2x + 15 = 0 \\ {x}^{2} - 2x - 15 = 0 \\ po \: \: \: teoreme \: \: \: vieta \\ {x}^{2} + bx + c = 0\\ x_{1} + x_{2} = - b\\ x_{1} x_{2} = c \\ x_{1}  +  x_{2} = 2 \\ x_{1} x_{2} = - 15  \\ x_{1} = 5 \\ x_{2} = - 3[/tex]

Первый корень не подходит

Ответ: х = - 3