Question

Решите неравенство
(Х/х-4)-(3/х)-(22/х²-4х)<=0

Answer 1

Объяснение:

$\frac{x}{x-4} -\frac{3}{x} -\frac{22}{x^2-4x}\leq 0\\\frac{x}{x-4} -\frac{3}{x} -\frac{22}{x*(x-4)}\leq 0\\\frac{x*x-3*(x-4)-22}{x*(x-4)} \leq 0\\\frac{x^2-3x+12-22}{x*(x-4)} \leq 0\\\frac{x^2-3x-10}{x*(x-4)} \leq 0\\\frac{x^2-5x+2x-10}{x*(x-4)}\leq 0\\\frac{x*(x-5)+2*(x-5)}{x*(x-4)}\leq 0\\\frac{(x-5)*(x+2)}{x*(x-4)} \leq 0.$

ОДЗ: х≠0      х-4≠0      х≠4.

-∞__+__-2__-__0__+__4__-__5__+__+∞

Ответ: х∈[-2;0)U(4;5].