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Math Help - Factor and Simplify

  1. #1
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    Factor and Simplify

    Factor and simplify. Express the answer as a fraction without negative exponents:

    2x(2x-1)^(-1/2) - 2(2x-1)^(1/2)
    Last edited by dc52789; January 27th 2009 at 12:45 PM. Reason: Forgot the negative sign.
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    Quote Originally Posted by dc52789 View Post
    Factor and simplify. Express the answer as a fraction without negative exponents:

    2x(2x-1)^(1/2) - 2(2x-1)^(1/2)
    If your question is
    2x\sqrt{2x-1}-2\sqrt{2x-1}
    than
    =(2x-2)\sqrt{2x-1}

     <br />
=(2x-2)(2x-1)^{\frac{1}{2}}<br />
    which seems to be your answer
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  3. #3
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    Ohh...I just edited my equation because I thought I placed the negative sign on the 1/2 square.
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  4. #4
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by dc52789 View Post
    Factor and simplify. Express the answer as a fraction without negative exponents:

    2x(2x-1)^(-1/2) - 2(2x-1)^(1/2)
    so your question now is
     <br />
\frac{2x}{\sqrt{2x-1}}-2\sqrt{2x-1}<br />
     <br />
=\frac{2x-2\sqrt{2x-1}\sqrt{2x-1}}{\sqrt{2x-1}}<br />
     <br />
=\frac{2x-4x+2}{\sqrt{2x-1}}<br /> <br />
     <br />
=\frac{2-2x}{\sqrt{2x-1}}<br />

    Multiplying numerator and denominator by  (2x-1)^\frac{1}{2}to convert the negative powers into positive

     <br />
=\frac{(2-2x)\sqrt{2x-1}}{{\sqrt{2x-1}}^2}<br />
     <br /> <br />
Ans=\frac{2(1-x)(2x-1)^{\frac{1}{2}}}{2x-1}<br />
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