algebra precalculus - how to solve algebraic fractions?

The question is

$$1/2n = 1 - 1/n$$

what i did was i first added the 1/n and tried to simplyfy it

$$1/2n + 1/n = 1$$
$$1n/2n(n) + 2n(1)/2n(n) = 2n(n)/2n(n)$$
I don't know if i did this right, i remember teacher telling me to use factored form.
and this is what i got
$$3n/2n(n) = 2n^2/2n(n)$$ than i multiplied 2n(n) from both sides getting
$$0 = 2n^2 - 3n$$
I won't be able to get zeroes from this or did i do the whole thing wrong