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Homework Help: Slope of a tangent line

  1. Sep 16, 2008 #1
    Find the slope of the functions graph at the given point.

    F(x) = x / x-2 point (3,3)

    f(x+h) - f(x) / h is what we have to use to find the answer.

    so ive plugged it all in and have came to this..

    ((3+h) / (3+h-2)) - 3 / h

    I need some help with my simplification skills. I do not know how to get rid of a fraction in a fraction in this case im guessing. Where would I need to go next?
  2. jcsd
  3. Sep 16, 2008 #2


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    By lack of brackets (and by the question) I assume you mean
    [tex]\frac{\frac{3+h}{3 + h - 2} - 3}{h}[/tex]

    You can start by simplifying 3 + h - 2.
    Next, look at the numerator
    [tex]\frac{3 + h}{3 + h - 2} - 3 [/tex]
    and write it as a single fraction:
    [tex]\frac{...}{3 + h - 2}[/tex]

    Then you have something of the form
    [tex]\frac{a}{b} / c[/tex]
    multiply by 1 in the form: b/b which will give you
    [tex]\frac{ab}{b} / (bc) = a / (bc)[/tex]
  4. Sep 16, 2008 #3
    Thank you that is what I meant.
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