$(sin x - cos x +1)/(sin x + cos x -1)$
$(sin x - cos x +1)/(sin x + cos x -1)$
$\frac{\sin x - \cos x + 1}{\sin x + \cos x - 1} = \frac{\sin x - (\cos x - 1)}{\sin x + (\cos x - 1)} \cdot \frac{\sin x - (\cos x - 1)}{\sin x - (\cos x - 1)}...$
you can also multiply $\frac{\sin x + (\cos x - 1)}{\sin x + (\cos x - 1)}$ instead.