Question

Сократите дробь
2/x-4 - x+8/x²-16 - 1/x

Answer 1

$\dfrac2{x-4}-\dfrac{x+8}{x^2-16}-\dfrac1x=\dfrac{2}{x-4}-\dfrac{x+8}{(x-4)(x+4)}-\dfrac1x=\\\\=\dfrac{2(x+4)-x-8}{(x-4)(x+4)}-\dfrac1x=\dfrac{x(2x+8-x-8)-(x-4)(x+4)}{x(x^2-16)}=\\\\=\dfrac{2x^2+8x-x^2-8x-x^2+16}{x^3-16x}=\dfrac{16}{x^3-16x}$