Question

Решите неравенство 2x^3-8x^2+4x-12/x^2-4x<=2x-1/x-2+3/x

Answer 1

(2x³-8x²+4x-12)/x(x-4)≤(2x³-4x²-x+3x-6)/x(x-2)
(2x³-8x²+4x-12)/x(x-4)≤(2x³-4x²+2x-6)/x(x-2)
(2x³-8x²+4x-12)/x(x-4)-(2x³-4x²+2x-6)/x(x-2)≤0
(2x^4-4x³-8x³+16x²+4x²-8x-12x+24-2x^4+8x³+4x³-16x²-2x²+8x+6x-24)/x(x-4)(x-2)≤0
(2x²-6x)/x(x-4)(x-2)≤0
2x(x-3)/x(x-4)(x-2)≤0
2(x-3)/(x-4)(x-2)≤0 , x≠0
x=3  x=4  x=2
         _                               +                  _                +
------(0)---------------(2)----------[3]--------------(4)-----------------
x∈(-∞;0) U (0;2) U [3;4)

Answer 2

спасибо!