$\begin{array}{1 1} kt = \large\frac{n}{n-1}\big(\large\frac{1}{[A]^{n-1}} - \large\frac{1}{[A_0]^{n-1}}\big) \\ kt = \large\frac{1}{n}\big(\large\frac{1}{[A]^{n-1}} - \large\frac{1}{[A_0]^{n-1}}\big) \\ kt = \large\frac{1}{n-1}\big(\large\frac{1}{[A]^{n-1}} - \large\frac{1}{[A_0]^{n-1}}\big) \\ kt = (n-1)\big(\large\frac{1}{[A]^{n-1}} - \large\frac{1}{[A_0]^{n-1}}\big)\end{array}$