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Math Help - Radicals

  1. #1
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    Radicals

    How do you do this?

    1/(1 - x) + 1/(1+√x) = 1/(1-√x)
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  2. #2
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    Quote Originally Posted by Trentt View Post
    How do you do this?

    1/(1 - x) + 1/(1+√x) = 1/(1-√x)
    1/(1-x)=1/(1-√x)-1/(1+√x)

    1/(1-x)=(1+√x-1+√x)(1-x)=2√x/(1-x)

    1=2√x

    1/2=√x

    x=1/4
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  3. #3
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    Hello, Trentt!

    Welcome aboard!


    1/(1 - x) + 1/(1 + √x) .= .1/(1 - √x)

    First, note that: .(1 - √x)(1 + √x) .= .1 - x

    . . . . . . . . . .1 . . . . . 1 . . . . . . .1
    We have: . ------ + --------- .= .--------
    . . . . . . . . 1 - x . . 1 + √x . . . 1 - √x


    Multiply through by (1 + √x)(1 - √x):

    . . . . . 1 + 1 - √x . = . 1 + √x

    And we have: . 2√x .= .1 . . √x .= . . . x .= .

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  4. #4
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    Care to explain Perfect Hacker? I really have no clue what you're doing...

    EDIT:Has been explained
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  5. #5
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    Quote Originally Posted by Soroban View Post


    Multiply through by (1 + √x)(1 - √x):

    . . . . . 1 + 1 - √x . = . 1 + √x


    Could you explain this step---this is the confusing part to me. And also can you explain why you chose (1 + √x)(1 - √x) to multiply the equation by?
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  6. #6
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    Quote Originally Posted by Trentt View Post
    Could you explain this step---this is the confusing part to me. And also can you explain why you chose (1 + √x)(1 - √x) to multiply the equation by?
    Soroban multiplies through by (1+sqrt(x))(1-sqrt(x)) because:

    1-x = (1+sqrt(x))(1-sqrt(x)),

    so if you multiply both sides by this each of the terms leaves a simple
    term in sqrt(x):

    [1+sqrt(x))(1-sqrt(x)] [1/(1-x)]=(1-x)/(1-x) =1


    [1+sqrt(x))(1-sqrt(x)] [1/(1+sqrt(x))]=(1-sqrt(x))

    [1+sqrt(x))(1-sqrt(x)] [1/(1-sqrt(x))]=(1+sqrt(x))

    so after multiplying through you are left with the equation:

    1 + (1-sqrt(x)) = (1+sqrt(x)),

    orL

    2 sqrt(x) = 1

    RonL
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