2) x+1/x-2 - 5/x+2 = 12/x^2-4 + 1
x+1/x-2 -5/x+2 =12/(x-2)(x+2) + (x-2)(x+2)/(x-2)(x+2)
(x+1)(x+2) - 5(x-2) = 12 + (x-2)(x+2)
x^2+2x+x+2 - 5x+10 = 12 + x^2+2x-2x-4
x^2+2x+x- 5x-x^2-2x+2x=12+4-2-10
-2x = 4
x =-2
4) 3/x+2 + 9/(x+2)(x-1) = 1/x-1
3(x-1) + 9 = x+2
3x-3 + 9 =x+2
3x-x =2+3-9
2x =-4
x =-2
6)x+2/x+3 - x+1/x-1 = 4/(x+3)(x-1)
(x+2)(x-1) - (x+1)(x+3) = 4
x^2-x+2x-2-x^2-3x-x-3 = 4
-5x-5 =4
-5x-5-4 =0
-5x-9 =0
=>-5x-9=0 => x=9/-5
8) x-1/x+3 -x/x-3 = 7x-3/9-x^2
x-1/x+3 -x/x-3 = 7x-3/(3-x)(3+x)
x-1/x+3 -x/x-3 = -7x+3/(x-3)(x+3)
(x-1)(x-3) - x(x+3) = -7x+3
x^2-3x-x+3-x^2-3x=-7x+3
-7x+3 =-7x+3
-7x+7x =3-3
0x =0
=> x =0
10) x+4/2x^2-5x+2 + x+1/2x^2-7x+3 = 2x+5/2x^2-7x+3
x+4/2x^2-5x+2 + (x+1-2x-5)/2x^2-7x+3 =0
x+4/2x^2-5x+2 + -x-4/2x^2-7x+3 =0
x+4/(2x-1)(x-2) + -x-4/(2x-1)(x-3) =0
(x+4)(x-3) + (-x-4)(x-2) = 0
x^2-3x+4x-12 -x^2+2x-4x+8 = 0
-x-4 =0
=> x =-4