How would I factor $x(1-\delta_1 - \delta_3) + y(1-\delta_2-\delta_3)$ into the following:
$(x+y)\left[1- \dfrac{x}{x+y}(\delta_1+\delta_3) - \dfrac{y}{x+y}(\delta_2+\delta_3) \right]$
I basically want the form $(x+y)(1 - \text{something})$.
It might help to firstly factor the $x+y$ and then do some arithmetic to get $1- \text{something}$, but I want to know how the $x+y$ is factored.
Maybe I just don't know this technique of factoring.
The given expression is $x+y -(\delta_1+\delta_3)x-(\delta_2+\delta_3)y$. So you can write it as $(x+y) \frac { (x+y) -(\delta_1+\delta_3)x-(\delta_2+\delta_3)y}{x+y}$. In the fraction just divide each of the three terms by $x+y$.