1. $$ \frac{2}{a} + \frac{3}{a-1} $$

$$\frac{2}{a} + \frac{3}{a-1} = \frac{2(a-1) + 3a}{a(a-1)} = \frac{2a - 2 + 3a}{a(a-1)} = \frac{5a - 2}{a(a-1)}$$