1)1/x-1=2/x+1 2)x/x-5=x-2/x-6
1/x-1=2/x+1,x≠1,x≠-1 x/x-5=x-2/x-6,x≠5,x≠6
x+1=2(x-1) x*(x-6)=(x-2)*(x-5)
x+1=2x-2 x^2-6x=x^2-5x-2x+10
x-2x=-2-1 -6x=-5x-2x+10
-x=-3 -6x=-7x+10
x=3,x≠1,x≠-1 -6x+7x=10
x=3 x=10,x≠5,x≠6
3) 3/y-2=2/y-3 x=10
3/y-2=2/y-3,y≠2,y≠3 4)z+1/z-1=z-5/z-3
3(y-3)=2(y-2) z+1/z-1=z-5/z-3,z≠1,z≠3
3y-9=2y-4 (z+1)*(z+3)=(z-5)*(z-1)
3y-2y=-4+9 z^2-3z+z-3=z^2-z-5z+5
y=-4+9 -3z+z-3=-z-5z+5
y=5,y≠2,y≠3 -2z-3=-6z+5
y=5 -2z+6z=5+3
5)3x-1/3x+1=2- x-3/x+3 4z=5+3
3x-1/3x+1=2- x-3/x+3,x≠-1/3,x≠-3 4z=8
3x-1/3x+1 + x-3/x+3=2 z=2,z≠1,z≠3
(x+3)*(3x-1)+(3x+1)*(x-3)/(3x+1)*(x+3)=2 z=2
3x^2-x+9x-3+3x^2-9x+x-3/(3x+1)*9x+3)=2 6)2- 3x/3x-2=2x-9/2x-5
6x^2-6/(3x+1)*(x+3)=2 2- 3x/3x-2=2x-9/2x-5,x≠2/3,x≠5/2
6x^2-6=2(3x+1)*(x+3) - 3x/3x-2 - 2x-9/2x-5=-2
6x^2-6=(6x+2)*(x+3) - 3x*(2x-5)+(3x-2)*(2x-9)/(3x-2)*(2x-5)=-2
6x^2-6=6x^2+18x+2x+6 - 6x^2-15x+6x^2-27x-4x+18/(3x-2)*(2x-5)=-2
-6=18x+2x+6 - 12x^2-46x+18/(3x-2)*(2x-5)=-2
-6=20x+6 -(12x^2-46x+18)=-2(3x-2)*(2x-5)
-20x=6+6 -12x^2+46x-18=(-6x+4)*(2x-5)
-20x=12 -12x^2+46x-18=-12x^2+30x+8x-20
x=- 3/5,x≠-1/3,x≠-3 -12x^2+46x-18=-12x^2+38x-20
x=- 3/5=-0,6 46x-18=38x-20
7)3x-5/x-1 - 2x-5/x-2=1 46x-38x=-20+18
3x-5/x-1 - 2x-5/x-2=1,x ≠1,x≠2 8x=-2
(x-2)*(3x-5)-(x-1)*(2x-5)/(x-1)*(x-2)=1 x=- 1/4,x≠2/3,x≠5/2
3x^2-5x-6x+10-(2x^2-5x-2x+5)/(x-1)*(x-2)=1 x=- 1/4=-0,25
3x^2-5x-6x+10-(2x^2-7x+5)/(x-1)*(x-2)=1 8)9x-7/3x-2 - 4x-5/2x-3=1 3x^2-5x-6x+10-2x^2+7x-5/(x-1)*(x-2)=1 9x-7/3x-2 - 4x-5/2x-3=1,x≠2/3,x≠3/2
x^2-4x+5/(x-1)*(x-2)=1 (2x-3)*(9x-7)-(3x-2)*(4x-5)/(3x-2)*(2x-3)=1
x^2-4x+5=(x-1)*(x-2) 18x^2-14x-27x+21-(12x^2-15x-8x+10)/(3x-2)*(2x-3)=1
x^2-4x+5=x^2-2x-x+2 18x^2-14x-27x+21-(12x^2-23x+10)/(3x-2)*(2x-3)=1
-4x+5=-2x-x+2 18x^2-14x-27x+21-12x^2+23x-10/ (3x-2)*(2x-3)=1
-4x+5=-3x+2 6x^2-18x+11/(3x-2)*(2x-3)=1
-4x+3x=2-5 6x^2-18x+11=(3x-2)*(2x-3)
-x=-3 6x^2-18x+11=6x^2-9x-4x+6
x=3,x≠1,x≠2 -18x+11=-9x-4x+6
x=3 -18x+11=-13x+6
9) 8/3x-3 - 2+x/x-1=5/2-2x - 5/18 -18x+13x=6-11
8/3x-3 - 2+x/x-1=5/2-2x - 5/18,x≠1 -5x=-5
8/3x-3 - 2+x/x-1 - 5/2-2x=- 5/18 x=1,x≠2/3,x≠3/2
8/3(x-1) - 2+x/x-1 - 5/2(1-x)=- 5/18 x=1
8/3(x-1) - 2+x/x-1 - 5/2*(-(x-1))=-5/18 10)14/3x-12 - 2+x/x-4=3/8-2x - 5/6
8/3(x-1) - 2+x/x-1 + 5/2*(x-1)=-5/18 14/3x-12 - 2+x/x-4=3/8-2x - 5/6,x≠4
16-6(2+x)+15/6(x-1)=- 5/18 14/3x-12 - 2+x/x-4 - 3/8-2x=- 5/6
16-12-6x+15/6(x-1)= - 5/18 14/3(x-4) - 2+x/x-4 - 3/2(4-x)=- 5/6
19-6x/6(x-1)= - 5/18 14/3(x-4) - 2+x/x-4 - 3/2*((-4-x))=- 5/6
18(19-6x)=-30(x-1) 14/3(x-4) - 2+x/x-4 + 3/2*(4-x)=- 5/6
342-108x=-30x+30 28-6(2+x)+9/6(x-4)=- 5/6
-108x+30x=30-342 28-12-6x+9/6(x-4)=- 5/6
-78x=-312 25-6x/6(x-4)=- 5/6
x=4,x≠1 6(25-6x)=-30(x-4)
x=4 150-36x=-30x+120
11)x+5/3x-6 - 1/2=2x-3/2x-4 -36x+30x=120-150
x+5/3x-6 - 1/2=2x-3/2x-4,x≠2 -6x=-30
x+5/3x-6 - 2x-3/2x-4=1/2 x=5,x≠4
x+5/3(x-2) - 2x-3/2(x-2)=1/2 x=5
2(x+5)-3(2x-3)/6(x-2)=1/2 12)10/3 - 7x+2/6x+18=2+ 3x-1/4x-12
2x+0-6x+9/6(x-2)=1/2 10/3 - 7x+2/6x+18=2+ 3x-1/4x-12,x≠-3
-4x+19/6(x-2)=1/2 - 7x+2/6x+18 - 3x-1/4x+12=2- 10/3
2(-4x+19)=6(x-2) - 7x+2/6(x+3) - 3x-1/4(x+3)=- 4/3
-8x+38=6x-12 2(7x+2)+3(3x-1)/12(x+3)=- 4/3
-8x-6x=-12-38 - 14x+4+9x-3/12(x+3)=- 4/3
-14x=-50 - 23x+1/12(x+3)=- 4/3
x=25/7,x≠2 -3(23x+1)=-48(x+3)
x=25/7=3 4/7≈3,57143 -69x+3=-48x-144
13)2x-1/2x+1=2x+1/2x-1+8/1-4x^2 -69x+48x=-144+3
2x-1/2x+1=2x+1/2x-1+8/1-4x^2,x≠- 1/2,x≠1/2 -21x=-141
2x-1/2x+1 - 2x+1/2x-1 - 8/1-4x^2=0 x=47/7,x≠-3
2x-1/2x+1 - 2x+1/2x-1 - 8/(1-2x)*(1+2x)=0 x=47/7=6 5/7≈6,71429
2x-1/2x+1 - 2x+1/2x-1 - 8/-(2x-1)*(1+2x)=0 15)x^2-3/1-x^2 + x+1/x+1=4/1+x
2x-1/2x+1 - 2x+1/2x-1 + 8/(2x-1)*(1+2x)=0 x^2-3/1-x^2 + x+1/x+1=4/1+x,x≠
(2x-1)^2-(2x+1)^2+8/(2x-1)*(2x+1)=0 ≠-1,x≠1
(-2)*4x+8/(2x-1)*(2x+1)=0 x^2-3/1-x^2 +1=4/1+x
-8x+8/(2x-1)*(2x+1)=0 x^2-3/1-x^2 - 4/1+x=-1
-8x+8=0 x^2-3/(1-x)*(1+x) - 4/1+x=-1
-8x=-8 x^2-3-4(1-x)/(1-x)*(1+x)=-1
x=1,x≠- 1/2,x≠1/2 x^2-3-4+4x/(1-x)*(1+x)=-1
x=1 x^2-7+4x/(1-x)*(1+x)=-1
x^2-7+4x=-(1-x)*(1+x)
x^2-7+4x=-(1-x^2)
x^2-7+4x=-1+x^2
-7+4x=-1
4x=-1+7
4x=6
x=3/2,x≠-1,x≠1
x=3/2=1 1/2=1,5