Algebra help please :)

express k in terms of n

k(n - 1) / [k(1 - n) - 1] = (2 - n) / n

would u please show working
thank u

k(n - 1) / [k(1 - n) - 1] = (2 - n) / n

kn(n - 1) = (2 - n)[k(1 - n) - 1] = k(2 - n)(1 - n) + n - 2

kn(n - 1) - k(2 - n)(1 - n) = n - 2

k[n(n - 1) - (2 - n)(1 - n)] = n - 2

k = (n - 2) / [n(n - 1) + (2 - n)(n - 1)] = (n - 2) / [(n - 1)(n + 2 - n)]

k = (n-2) / 2(n - 1)