Question

1/х+6+3/х2-6х=72/х3-36х решите пожалуйста

Answer 1

Ответ:

$x = 9$

Объяснение:

$frac{1}{x + 6} + frac{3}{ {x}^{2} - 6x} = frac{72}{ {x}^{3} - 36x } \ \ x≠ - 6 \ x≠0 \ x≠6 \ \ frac{1}{x + 6} + frac{3}{ {x}^{2} - 6x} - frac{72}{ {x}^{3} - 36x } = 0 \ frac{1}{x + 6} + frac{3}{x(x - 6)} - frac{72}{x( x + 2)(x - 2)} = 0 \ frac{x(x - 6) + 3(x + 6) - 72}{x(x - 6)(x + 6)} = 0 \ frac{ {x}^{2} - 6x + 3x + 18 - 72 }{x(x - 6)(x +6)} = 0 \ frac{ {x}^{2} - 3x - 54}{x(x - 6)(x +6)} = 0 \ frac{ {x}^{2} + 6x - 9x - 54}{x(x - 6)(x + 6)} = 0 \ frac{x(x + 6) - 9(x + 6)}{x( x - 6)(x + 6)} = 0 \ frac{(x + 6)(x - 9)}{x(x - 6)(x + 6)} = 0 \ frac{x - 9}{x - 6} = 0 \ x - 9 = 0 \ x = 9$