Question

Упростите дробь (если можно,решите на листе и сфотографируйте)

Answer 1

$\frac{2}{x-4}- \frac{x+8}{x^2-16} - \frac{1}{x} = \frac{2}{x-4}- \frac{x+8}{x^2-4^2} - \frac{1}{x} = \\ \frac{2}{x-4}- \frac{x+8}{(x-4)(x+4)} - \frac{1}{x} =\frac{2x(x+4)}{x(x-4)(x+4)}- \frac{x(x+8)}{x(x-4)(x+4)} - \frac{(x-4)(x+4)}{x(x-4)(x+4)} = \\ \frac{2x(x+4)-x(x+8) -(x-4)(x+4)}{x(x-4)(x+4)} = \frac{2x^2+8x-x^2-8x -x^2+16}{x(x-4)(x+4)} = \\ \frac{16}{x(x-4)(x+4)} = \frac{16}{x(x^2-16)} = \frac{16}{x^3-16}$