Find the difference quotient $\displaystyle \frac {f(a + h) - f(a)}{h}$

for $\displaystyle \frac {x+3}{x+1}$

My issue is... I tried figuring it out MANY ways, but it just seems that it's so messy. I don't feel like i've done it correctly. I have to get to class in a few minutes, or i'd post the solutions i've gotten. Any piece of information would help.