a: 1/x-2=1/x-2
2/2x-4=2/2(x-2)=1/x-2
3/3x-6=3/3(x-2)=1/x-2
b: 1/x+4=(2x-8)/2(x+4)(x-4)
1/2x+8=(x-4)/2(x+4)(x-4)
\(\dfrac{3}{x-4}=\dfrac{3\cdot2\cdot\left(x+4\right)}{2\cdot\left(x-4\right)\left(x+4\right)}=\dfrac{6x+24}{2\left(x-4\right)\left(x+4\right)}\)
c: 1/x^2-1=1/(x-1)(x+1)
2/x-1=2(x+1)/(x-1)(x+1)=(2x+2)/(x-1)(x+1)
2/x+1=2(x-1)/(x+1)(x-1)=(2x-2)/(x-1)(x+1)
d: 1/2x=(x-2)/2x(x-2)
2/x-2=2*2x/2x(x-2)=4x/2x(x-2)
3/2x(x-2)=3/2x(x-2)