Question

(x-5)<(8/(x+2)) Решите неравенство

Answer 1

x-5<8/(x+2)   ОДЗ: x+2≠0    x≠-2
x-5-(8/(x+2))<0
(x-5)*(x+2)-8<0
x²-5x+2x-10-8<0
x²-3x-18<0
x²-3x-18=0   D=81
x₁=6   x₂=-3
(x-6)(x+3)<0
-∞____+____-3____-____6____+_____+∞
x∈(-3;6).
Согласно ОДЗ:
x∈(-3;-2)U(-2;6).