So, when we're tasked with things like this, rewriting everything in terms of sine and cosine and combining fractions often trivializes things, so doing just that gives us:
[tex] \frac{\frac{1}{\cos{x}}-\frac{1}{\sin{x}}}{\frac{\cos{x}}{\sin{x}}-1}= \\\frac{\frac{=(\cos{x}-\sin{x})}{\cos{x}\sin{x}}}{\frac{\cos{x}}{\sin{x}}-\frac{\sin{x}}{\sin{x}}}=\\\frac{-(\cos{x}-\sin{x})}{\cos{x}\sin{x}}*\frac{\sin{x}}{\cos{x}-\sin{x}}=\\-\frac{1}{\cos{x}} [/tex]
So out expression is 1/cos(x).
