1.
(2x-3)/(x²-4x+4)=(2x-3)/(x-2)².
2. (x-1)/(x²-2x)=(x-1)/(x*(x-2)).
3. (2x-3)/(x-2)²-(x-1)/(x*(x-2))=(x*(2x-3)-(x-1)(x-2))/(x*(x-2)²)=
=(2x²-3x-(x²-3x+2))/(x*(x-2)²)=(2x²-3x-x²+3x-2)/(x*(x-2)²)=(x²-2)/(x*(x-2)²).
4. (x²-2)/(x³-4x)=(x²-2)/(x*(x²-4))=(x²-2)/(x*(x-2)(x+2)).
5. (x²-2)/(x*(x-2)²):(x²-2)/(x*(x-2)(x+2))=(x²-2)(x*(x-2)(x+2)/((x²-2)(x*(x-2)²=(x+2)/(x-2).