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Math Help - Derivative

  1. #1
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    Derivative

    find the equation of the tangent line to  f(x) = x+\sqrt{x} at (4,6)


    \frac{(x+\sqrt{x})-(4+\sqrt{4})}{x-4}

    =  \frac{x-4+\sqrt{x}-\sqrt{4}}{x-4}

    why am I havin so much trouble getting that denominator out of there
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  2. #2
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    \frac{(x + \sqrt{x}) - (4 + \sqrt{4})}{x-4} =

    \frac{x + \sqrt{x} - 6}{x-4} =

    \frac{(\sqrt{x}  +  3)(\sqrt{x}  - 2)}{(\sqrt{x}  + 2)(\sqrt{x}  - 2)}  =

    \frac{\sqrt{x}  +  3}{\sqrt{x}  + 2}

    now take the limit
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