Simplify (cot(x)+2cos(x))/(csc(x)-sin(x))

$\frac{\cot (x) + 2 \cos (x)}{\csc (x) - \sin (x)}$

Simplify the numerator.

Rewrite $\cot (x)$ in terms of sines and cosines.

$\frac{\frac{\cos (x)}{\sin (x)} + 2 \cos (x)}{\csc (x) - \sin (x)}$

Factor $\cos (x)$ out of $\frac{\cos (x)}{\sin (x)} + 2 \cos (x)$ .

Factor $\cos (x)$ out of $\frac{\cos (x)}{\sin (x)}$ .

$\frac{\cos (x) \frac{1}{\sin (x)} + 2 \cos (x)}{\csc (x) - \sin (x)}$

Factor $\cos (x)$ out of $2 \cos (x)$ .

$\frac{\cos (x) \frac{1}{\sin (x)} + \cos (x) \cdot 2}{\csc (x) - \sin (x)}$

Factor $\cos (x)$ out of $\cos (x) \frac{1}{\sin (x)} + \cos (x) \cdot 2$ .

$\frac{\cos (x) (\frac{1}{\sin (x)} + 2)}{\csc (x) - \sin (x)}$

Rewrite $\csc (x)$ in terms of sines and cosines.

$\frac{\cos (x) (\frac{1}{\sin (x)} + 2)}{\frac{1}{\sin (x)} - \sin (x)}$

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\frac{\cos (x) (\csc (x) + 2)}{\frac{1}{\sin (x)} - \sin (x)}$

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\frac{\cos (x) (\csc (x) + 2)}{\csc (x) - \sin (x)}$