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Math Help - horray for difference quotients

  1. #1
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    horray for difference quotients

    Consider the function below.
    Evaluate the difference quotient for the given function. Simplify your answer.


    and here is my attempt
    (((x+7)/(x+5))-((5+7)/(5+5)))/x-5

    first, I just did the math

    <br />
(((x+7)/(x+5))-(6/5))/x-5

    then the only thing I could think of was to do me some rationalizing

    (-6(x+5)+5(x+7))/(5(x+5)(x-5))

    and some nice little simplification

    (5-x)/(5x^2 -125)

    I have a sneaky notion that this is incorrect.
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  2. #2
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    Hello,
    Quote Originally Posted by leftyguitarjoe View Post
    (-6(x+5)+5(x+7))/(5(x+5)(x-5))

    and some nice little simplification

    (5-x)/(5x^2 -125)

    I have a sneaky notion that this is incorrect.
    Nope, this is correct !
    But you should have stayed at this step :
    \frac{-6(x+5)+5(x+7)}{5(x+5)(x-5)}

    Don't expand the denominator yet and calculate the numerator
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