posted by Taylor .
3y/y^-2y - y/y^-2y=4/y^-2y
Put y =2 in the original equation on each side, and see if each side equals the other side.
y=2 should immediately be discarded, since fractions with y-2 in the denominator are not defined.
The steps should be
3y/y(y-2) - (y-2)/y(y-2) = 4/y(y-2)
3y-y+2 = 4
2y = 2
y = 1