Question

1. 2/x-3=7/x+1
2. (x-5)(2x+6)=0
3. x(x+3)=4
4. 18-x^2=14
Помогите пожалуйста решить эти уравнения.
Заранее спасибо

Answer 1

$\frac{2}{x - 3} = \frac{7}{x + 1} \\ \frac{2}{x - 3} - \frac{7}{x + 1} = 0 \\ \frac{2(x + 1) - 7(x - 3)}{(x + 1)(x - 3)} = 0 \\ \frac{2x + 2 - 7x + 21}{(x + 1)(x - 3)} = 0 \\ \frac{23 - 5x}{(x + 1)(x - 3)} = 0 \\ 23 - 5x = 0 \\ (x + 1)(x - 3)neravno \: 0 \\ 5x = 23 \\ x \: neravno \: - 1 \\ x \: neravno \: 3 \\ x = 4.6$
(х-5)(2х+6)=0
х+5=0. 2х+6=0
х=-5 и х=-3

х(х+3)=0
х=0 и х+3=0
х=0 и х=-3

$18 - {x}^{2} = 14 \\ 4 - {x}^{2} = 0 \\ (2 - x)(2 + x) = 0 \\ x = 2 \: and \: x = - 2$