1)
(x²+x-45)/(x-6)≤(3x+1)/2 ОДЗ: x-6≠0 x≠6
(x²+x-45)/(x-6)-(3x+1)/2≤0
(2*(x²+x-45)-(3x+1)(x-6))/(2*(x-6))≤0
(2x²+2x-90-3x²+17x+6)/(2*(x-6))≤0
(-x²+19x-84)/(2*(x-6))≤0 |×(-2)
(x²-19x+84)/(x-6)≥0
x²-19x+84=0 D=25 √D=5
x₁=12 x₂=7 ⇒
(x-12)(x-7)/(x-6)≥0
-∞______-_____6_____+_____7_____-_____12_____+_____+∞
Ответ: x∈(6;7]U[12;+∞).
2)
(5x+4)/(5x²-6x+1)<1/(x-2)<br>ОДЗ: x-2≠0 x≠2 5x²-6x+1≠0 D=4 x₁≠1 x₁≠0,2
(5x+4)/(5x²-6x+1)-1/(x-2)<0<br>((5x+4)(x-2)-5x²+6x-1)/((5x²-6x+1)(x-2))<0<br>(5x²-6x-8-5x²+6x-1)/(5*(x-1)(x-0,2)(x-2))<0<br>-9/(5*(x-1)(x-0,2)(x-2))<0 |×(-5/9)<br>1/((x-0,2)(x-1)(x-2)>0
-∞____-____0,2___+____1____-____2____+____+∞
Ответ: x∈(0,2;1)U(2;+∞).