$$\begin{lgathered}\displaystyle \frac{y}{2x+2y} + \frac{x}{a-1}\cdot \frac{a-1}{2x+2y}= \frac{y}{2x+2y} + \frac{x}{2x+2y}=\\ \\ \\ = \frac{x+y}{2x+2y}= \frac{x+y}{2(x+y)}= \frac{1}{2}\end{lgathered}$$
$$\begin{lgathered}\displaystyle \frac{y}{2x+2y} + \frac{x}{a-1}\cdot \frac{a-1}{2x+2y}= \frac{y}{2x+2y} + \frac{x}{2x+2y}=\\ \\ \\ = \frac{x+y}{2x+2y}= \frac{x+y}{2(x+y)}= \frac{1}{2}\end{lgathered}$$