Question

1/х+6+3/х2-6х=72/х3-36х решите

Answer 1

$x = 9$

Объяснение:

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