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Thread: Factor and Simplify Algebraic Expression

  1. #1
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    Factor and Simplify Algebraic Expression

    I am doing some review questions for University and don't recall how to answer a question like this (my answer should only have positive exponents) .... Thanks!
    $\displaystyle
    (x+3)^\frac{-1}{3}
    $ $\displaystyle
    -(x+3)^\frac{-4}{3}
    $
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  2. #2
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    Quote Originally Posted by bearhug View Post
    I am doing some review questions for University and don't recall how to answer a question like this (my answer should only have positive exponents) .... Thanks!
    $\displaystyle
    (x+3)^\frac{-1}{3}
    $ $\displaystyle
    -(x+3)^\frac{-4}{3}
    $
    $\displaystyle (x+3)^{-\frac{1}{3}} - (x+3)^{-\frac{4}{3}}$

    common factor for both terms is $\displaystyle (x+3)^{-\frac{4}{3}}$ ...

    $\displaystyle (x+3)^{-\frac{4}{3}}[(x+3) - 1]$

    $\displaystyle (x+3)^{-\frac{4}{3}}(x+2)$

    $\displaystyle \frac{x+2}{(x+3)^{\frac{4}{3}}}
    $
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  3. #3
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    Quote Originally Posted by bearhug View Post
    I am doing some review questions for University and don't recall how to answer a question like this (my answer should only have positive exponents) .... Thanks!
    $\displaystyle
    (x+3)^\frac{-1}{3}
    $ $\displaystyle
    -(x+3)^\frac{-4}{3}
    $
    $\displaystyle
    (x+3)^\frac{-1}{3}
    $ $\displaystyle
    -(x+3)^\frac{-4}{3}
    $=$\displaystyle \frac{1}{(x+3)^\frac{1}{3}}-\frac{1}{(x+3)^\frac{4}{3}}= \frac{(x+3)-1}{(x+3)^\frac{4}{3}}=\frac{x+2}{(x+3)^\frac{4}{3} }$
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