ОДЗ
x+3≥0⇒x≥-3
x-1≥0⇒x≥1
x-2≥0⇒x≥2
x∈[2;∞)
x+3<x-1+2√(x²-3x+2)+x-2
x+3-2x+3<2√(x²-3x+2)
6-x<2√(x²-3x+2)
36-12x+x²<4x²-12x+8
4x²-12x+8-36+12x-x²>0
3x²-28>0
(x-2√21/3)(x+2√21/3)>0
x<-2√21/3 U x>2√21/3
x∈(2√21/3;∞)
Если корень из всей дроби, то:
√6/√3=√2/√1=√2
если из 6:
√6/3=√6/√3^2(типо в квадрате)=√6/√9=√2/√3=3√2
2
a)(5-3x)/(x-3)(x+3)+(7x-1)/(2x(x+3)=(10x-6x²+7x²-21x-x+3)/[2x(x²-9)]=
=(x²-12x+3)/[2x(x²-9)]
b)1/2(x-y)²-(x-y-2)/4(x-y)²=(2-x+y+2)/4(x-y)²=(4-x+y)/4(x-y)²
3
a)7/a-4/(a-2b)-(a-b)/(a-2b)(a+2b)=(7a²-28b²-4a²-8ab-a²+ab)/[a(a²-4b²)]=
=(2a²-7ab-28b²)/[a(a²-4b²)]
b)(a²-a)/(a+1)(a²-a+1)-1/(1+a)=(a²-a-a²+a-1)/(a³+1)=-1/9a³+1)
4
a)(a+2)/2(a-2)-(a-2)/3(a+2)-(a²+4)/6(a-2)(a+2)=
=(3a²+6a+6a+12-2a²+4a+4a-8-a²-4)/6(a²-4)=20a/6(a²-4)=10a/3(a²-4)
a=-4
-40/3*(16-4)=-40/36=-10/9=-1 1/9
b)b/(a(a-b)+a/b(a+b)-(a²+b²)/a(a-b)(a+b)=(ab²+b³+a³-a²b-a²b-b³)/ab(a²-b²)=
=(ab²+a³-2a²b)/ab(a²-b²)=a(a²-2ab+b²)/ab(a²-b²)=(a-b)²/b(a-b)(a+b)=
(a-b)/b(a+b)
a=6;b=-1
(6+1)/[-1*(6-1)]=7/(-5)=-1,4
5
(a-2)/a(a+2)+(a+2)/a(a-2)-(2a²+8)/[a(a-2)(a+2)]=
=(a²-4a+4+a²+4a+4-2a²-8)/[a(a-2)(a+2)]=0