1
3x/(x+2)-|3-x|≤0
1)x>3
3x/(x+2)-x+3≤0
(3x-x²-2x+3x+6)/(x+2)≤0
(x²-4x-6)/9x+2)≥0
x²-4x-6=0
D=16+24=40
x1=(4-2√10)/2=2-√10 U x2=2=√10
x+2=0
x=-2
///////////////////////// //////////////////
_ + _ +
---------(-2)------------[2-√10]------(3)-------[2+√10]--------
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
x∈[2+√10;∞)
2)x≤3
3x/(x+2)-3+x≤0
(3x-3x-6+x²+2x)/(x+2)≤0
(x²+2x-6)/(x+2)≤0
x²+2x-6=0
D=4+24=28
x1=(-2-2√7)/2=-1-√7 U x2=-1+√7
x=-2
///////////////// ////////////////////
_ + _ +
----------[-1-√7]------------(-2)----------[-1+√7]--------[3]-------
/////////////////////////////////////////////////////////////////////////////
x∈(-∞;-1-√7] U (2;-1+√7]
Ответ x∈(-∞;-1-√7] U (2;-1+√7] U [2+√10;∞)
2
Возведем в квадрат
(x-5)²/(x+3)²-(x+4)²/(x-6)²≥0
[(x²-11x+30)²-(x²+7x+12)²]/(x+3)²(x-6)²≥0
(x²-11x+30-x²-7x-12)(x²-11x+30+x²+7x+12)/(x+3)²(x-6)²≥0
(18-18x)(2x²-4x+41)/(x+3)²(x-6)²≥0
36(x-1)(x²-2x+21)/(x+3)²(x-6)²≤0
x-1=0
x=1
x²-2x+21=0
D=4-84=-80⇒x∈R
x+3=0
x=-3
x-6=0
x=6
_ _ + +
-----------(-3)------------[1]---------------(6)---------
x∈(-∞;-3) U (-3;1]