Difference quotient help!

**shiznid12** · October 1st 2009, 02:23 PM

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

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

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.

**Danny** · October 1st 2009, 02:33 PM

Originally Posted by shiznid12

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

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

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.

$\frac{1}{h} \cdot \left(\frac{a+h+3}{a+h+1} - \frac {a+3}{a+1}\right) = \frac{1}{h} \cdot \frac{(a+h+3)(a+1) - (a+3)(a+h+1)}{(a+1)(a+h+1)}$ $= \frac{1}{h} \cdot \frac{-2h}{(a+1)(a+h+1)}$ $= \frac{-2}{(a+1)(a+h+1)}$

**pickslides** · October 1st 2009, 02:34 PM

Maybe divide it out first

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

Now try again.

**shiznid12** · October 1st 2009, 02:34 PM

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

Thanks A LOT!!!!!!

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