(x-4)/(x²-5x+6)+(x+2)/(x²+x-12)≥0
x²-5x+6=0
x1+x2=5 U x1*x2=6⇒x1=2 U x2=3
x²+x-12=0
x1+x2=-1 U x1*x2=-12⇒x1=-4 U x2=3
(x-4)/[(x-2)(x-3)]+(x+2)/[(x+4)(x-3)]≥0
(x²-16+x²-4)/[(x-2)(x-3)(x+4)]≥0
(2x²-20)/[(x-2)(x-3)(x+4)]≥0
2(x-√10)(x+√10)/[(x-2)(x-3)(x+4)]≥0
x=√10 x=-√10 x=2 x=3 x=-4
_ + _ + _ +
------------------(-4)----------[-√10]---------(2)---------(3)---------[√10]-----------
x∈(-4;-√10] U (2;3) U [√10;∞)