$F = \frac{R^2 / k}{(1 - R^2) / (n - k - 1)}$

$F = \frac{(1 - R^2) / k}{R^2 / (n - k - 1)}$

$F = \frac{R^2 (n - k - 1)}{k (1 - R^2)}$

$F = \frac{R^2}{1-R^2}$