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Math Help - rational exponents

  1. #1
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    rational exponents

    I can not get this. the left hand side simplifies to the right.

    -x^2(x^2+1)^{-3/2}+(x^2+1)^{-1/2} \Rightarrow (x^2+1)^{-3/2}

    I tried this but but then if I factor out (x^2+1) there are extra terms etc.

    -x^2(x^2+1)(x^2+1)^{-1/2}+(x^2+1)^{-1/2}=?
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  2. #2
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    Re: rational exponents

    \displaystyle \begin{align*} -x^2(x^2 + 1)^{-\frac{3}{2}} + (x^2 +1)^{-\frac{1}{2}} &= \frac{-x^2}{(x^2 + 1)^{\frac{3}{2}}} + \frac{1}{(x^2 + 1)^{\frac{1}{2}}} \\ &= \frac{-x^2}{(x^2 + 1)^{\frac{3}{2}}} + \frac{x^2 + 1}{(x^2 + 1)^{\frac{3}{2}}} \\ &= \frac{-x^2 + x^2 + 1}{(x^2 + 1)^{\frac{3}{2}}}   \\ &= \frac{1}{(x^2 + 1)^{\frac{3}{2}}} \\ &= (x^2 + 1)^{-\frac{3}{2}}\end{align*}
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  3. #3
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    Re: rational exponents

    thanks. that makes sense. I was over complicating things.
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