1. ## Difference quotient help!

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.

2. Originally Posted by shiznid12
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.
$\displaystyle \frac{1}{h} \cdot \left(\frac{a+h+3}{a+h+1} - \frac {a+3}{a+1}\right) = \frac{1}{h} \cdot \frac{(a+h+3)(a+1) - (a+3)(a+h+1)}{(a+1)(a+h+1)}$ $\displaystyle = \frac{1}{h} \cdot \frac{-2h}{(a+1)(a+h+1)}$$\displaystyle = \frac{-2}{(a+1)(a+h+1)}$

3. Maybe divide it out first

$\displaystyle \frac {x+3}{x+1} = \frac {2}{x+1}+1$

Now try again.

4. Ok... I see what I did now. I feel really stupid. lol

Thanks A LOT!!!!!!