2/221
a)(2x²+4x)(3x-x²)/(2x+5)³≤0
2x²(x+2)(x-3)/(2x+5)³≥0
x=0 x=-2 x=3 x=-2,5
_ + _ _ +
--------------(-2,5)-------[-2]------------[0]-------------[3]-----------------
x∈(-2,5;-2] U [3;∞) U {0}
b)(x+2)^4*(x+3)²/(x²-x+2)>0
x=-2 x=-3 x²-x+2=0 D=1-8=-7<0⇒x-любое<br>x∈(-∞;-3) U (-3;-2) U (-2;∞)
2.222
a)(3x+7)(x-3)²/(x-5)(x+5)<0<br>x=-2 1/3 x=3 x=5 x=-5
_ + _ _ +
--------------(-5)----------(-2 1/3)---------(3)------------(5)-----------------
x∈(-∞;-5) U (-2 1/3;5) U (3;5)
b)(x²-2x-1)/(2x-5)(x+2)²≤0
x²-2x-1=0 D=4+4=8 x1=1-√2 x2=1+√2
2x-5=0⇒x=2,5
x-3=0⇒x=3
_ _ + _ +
------------(-2)-------------[1-√2]----------[1+√2]----------(2,5)------------
x∈(-∞;-2) U (-2;1-√2] U [1+√2;;2,5)
2,223
a)1/(x+3)-1/(x-1)-1≤0
(x-1-x-3-x²+x-3x+3)/(x+3)(x-1)≤0
(x²+2x+1)/(x+3)(x-1)≥0
(x+1)²/(x+3)(x-1)≥0
x=-1 x=-3 x=1
+ _ _ +
-----------(-3)------------[-1]------------(1)----------------
x∈(-∞;-3) U (1;∞) U {-1}
b)2/(x-5)+1-2/(x+1)≥0
(2x+2+x²+x-5x-5-2x+10)/(x-5)(x+1)≥0
(x²-4x+7)/(x-5)(x+1)≥0
x²-4x+7=0 D=16-28=-12<0⇒x-любое<br>(x-5)(x+1)>0
x=5 x=-1
x∈(-∞;-1) U (5;∞)
2,224
a)(x-3)(2x+1)/x-(x+3)(x-1)/x<0<br>(2x²+x-6x-3-x²+x-3x+3)/x<0<br>(x²-7x)/x<0<br>x(x-7)/x<0<br>x-7<0,x≠0<br>x<7,x≠0<br>x∈(-∞;0) U (0;7)
b)3x+(x-1)/(2x-1)-(2x²-1)/(2x-1)≥0
(6x²-3x+x-1-2x²+1)/(2x-1)≥0
(4x²-2x)/(2x-1)≥0
2x(2x-1)/(2x-1)≥0
2x≥0,x≠0,5
x≥0,x≠0,5
x∈[0;0,5) U (0,5;∞)
2.226
a)(x+1)(x+2)/(x²+7x+12) -1≤0
(x²+2x+x=2-x²-7x-12)/(x²+7x+12)≤0
(5x+10)/(x²+7x+12)≥0
5x+10=0⇒x=-2
x²+7x+12=0 x1+x2=-7 U x1*x2=12⇒x1=-4 U x2=-3
_ + _ +
-------------(-4)-----------(-3)-----------[-2]--------------
x∈(-4;-3) U [-2;∞)
b)(x²+3x-13)/(x+3)(x-2)-2>0
(x²+3x-13-2x²+4x-6x+12)/(x+3)(x-2)>0
(x²-x+1)/(x+3)(x-2)>0
x²-x+1=0 D=1-4=-3⇒x-любое
(x+3)(x-2)>0
x=-3 x=2
x∈(-∞;-3) U (2;∞)