$( frac{1}{ x^{2}-7x+12 } + frac{x-4}{3-x} )$ × $sqrt{6x-x^{2} } leq 0$

ОДЗ
x²-7x+12=0
(x-3)(x-4)=0
x₁=3
x₂=4

3-x=0
x=3

6x-x²≥0
x(6-x)≥0
x(x-6)≤0
x∈[0;6]

$( frac{1}{(x-3)(x-4)} - frac{x-4}{x-3}) sqrt{x(6-x)} leq 0$
$frac{1-(x-4)(x-4)}{(x-3)(x-4)} * sqrt{x(6-x)} leq 0$
$frac{1- x^{2}+8x-16 }{(x-3)(x-4)} * sqrt{x(6-x)} leq 0$
$frac{- (x^{2}-8x+15) }{(x-3)(x-4)} * sqrt{x(6-x)} leq 0$
$frac{ (x^{2}-8x+15) }{(x-3)(x-4)} * sqrt{x(6-x)} geq 0$
D=8*8-4*15=4
x₁=(8-2)/2=3
x₂=(8+2)/2=5
$frac{ (x-3)(x-5)) }{(x-3)(x-4)} * sqrt{x(6-x)} geq 0$
$frac{x-5}{x-4}* sqrt{x(6-x)} geq 0$
x∈[5; +∞)
учитывая ОДЗ

х∈[5; 6]