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Math Help - Difference quotient help!

  1. #1
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    Difference quotient help!

    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.
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  2. #2
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    Quote Originally Posted by shiznid12 View Post
    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)}
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  3. #3
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    Maybe divide it out first

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

    Now try again.
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  4. #4
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    Ok... I see what I did now. I feel really stupid. lol

    Thanks A LOT!!!!!!
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