Prove that the fundamental unit of the real quadratic field $\mathbb{Q}(\sqrt{m^2 - 1})$ is $m+\sqrt{m^2 - 1}$ if $m^2-1$ is square free
I tried taking $a + b\sqrt{m^2-1}$ as an arbitrary unit and multiplied it with another unit $c + d\sqrt{m^2-1}$ to get some equations to work with, but it is going nowhere.
Any help will be appreciated.