Pregunta: Simplify the expression.

Given expression: $\frac{\cos \left(\varphi \right)-4}{\sin \left(\varphi \right)}+\frac{\sin \left(\varphi \right)}{\cos \left(\varphi \right)+4}$

We can write this as:

$\frac{\left((\cos \left(\varphi \right)-4)(\cos \left(\varphi \right)+4)\right)+(\sin \left(\varphi \right)\times \sin \left(\varphi \right))}{\sin \left(\varphi \right)(\cos \left(\varphi \right)+4)}$