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Math Help - Simplifying rational expressions 2

  1. #1
    Lil
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    Post Simplifying rational expressions 2

    How about this?  \frac{a-b}{a+b+2a^{\frac{1}{2}}b^{\frac{1}{2}}}:\frac{a^{-\frac{1}{2}}-b^{-\frac{1}{2}}}{a^{-\frac{1}{2}}+b^{-\frac{1}{2}}}
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  2. #2
    MHF Contributor harish21's Avatar
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    First of all,Are you taking ratio of those two terms?

    Secondly, Show your work!

    Also,

    a+b+2a^{\frac{1}{2}}b^{\frac{1}{2}}} = (\sqrt{a}+\sqrt{b})^2

    and

     \displaystyle{a^{-\frac{1}{2}} = \frac{1}{\sqrt{a}}}
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  3. #3
    Lil
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    ...=\frac{(a-b)*(\sqrt{a}+\sqrt{b})}{(\sqrt{a}+\sqrt{b})^2*(\sq  rt{a}-\sqrt{b})}=\frac{(a-b)}{(\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b})}=\frac{a-b}{a-b}=1
    But answer have to be -1. What's wrong?
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  4. #4
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by Lil View Post
    ...=\frac{(a-b)*(\sqrt{a}+\sqrt{b})}{(\sqrt{a}+\sqrt{b})^2*(\sq  rt{a}-\sqrt{b})}=\frac{(a-b)}{(\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b})}=\frac{a-b}{a-b}=1
    But answer have to be -1. What's wrong?
    \displaystyle{\frac{a^{-\frac{1}{2}}-b^{-\frac{1}{2}}}{a^{-\frac{1}{2}}+b^{-\frac{1}{2}}} =\frac{\sqrt{b}-\sqrt{a}}{\sqrt{b}+\sqrt{a}}}
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