Question

Помогите понять как решается:

Answer 1

$\frac{1}{x} + \frac{1}{x+5} = \frac{1}{6} ;$
$\frac{1}{x} + \frac{1}{x+5} - \frac{1}{6} = 0;$
$\frac{6(x+5) + 6x - x (x + 5)}{6x(x+5)} = 0;$ | * 6x (x + 5)
6 (x + 5) + 6x - x (x + 5) = 0
6x + 30 + 6x - x² - 5x = 0
- x² + 7x + 30 = 0
x² - 7x - 30 = 0
x₁ + x₂ = 7
x₁ * x₂ = - 30
x₁ = - 3; x₂ = 10

Ответ: x₁ = - 3; x₂ = 10