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Math Help - Solving for y

  1. #1
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    Solving for y

    How is y solved for in this equation?

    x=\frac{1-\sqrt{y}}{1+\sqrt{y}}
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  2. #2
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    Multiply both sides of the equation by 1/(1 + \sqrt{y}), then isolate \sqrt{y}. The rest will follow.
    Last edited by wonderboy1953; July 16th 2010 at 11:32 AM. Reason: correction
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  3. #3
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    Did you make a typo in that formula?
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  4. #4
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    Yes, should be multiplying both sides by (1 + \sqrt{y})
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  5. #5
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    x=\frac{1-\sqrt{y}}{1+\sqrt{y}}
    synthetically divide:
    x = \frac{2}{\sqrt{y}+1} - 1
    add 1:
    x + 1= \frac{2}{\sqrt{y}+1}
    multiply by that denominator and divide by x+1:
    \sqrt{y} + 1 = \frac{2}{x + 1}
    subtract 1:
    \sqrt{y} = \frac{2}{x + 1} - 1
    find common denominator and add:
     \sqrt{y} = \frac{-x + 1}{x+1}
    square both sides:
    y = \frac{(-x+1)^2}{(x+1)^2}
    factor out -1 from numerator:
     y = \frac{(-[x-1])^2}{(x+1)^2}
    distribute ^2:
    y = (-1)^2\frac{(x-1)^2}{(x+1)^2}
    -1*-1 = 1:
     y = \frac{(x-1)^2}{(x+1)^2}
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  6. #6
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    Quote Originally Posted by Mike9182 View Post
    x=\frac{1-\sqrt{y}}{1+\sqrt{y}}
    Another way:

    x(1 + SQRT[y]) = 1 - SQRT[y]

    x + xSQRT[y] = 1 - SQRT[y]

    xSQRT[y] + SQRT[y] = 1 - x

    SQRT[y](x + 1) = -1(x - 1)

    SQRT[y] / -1 = (x - 1) / (x + 1)

    y = [(x - 1) / (x + 1)]^2
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  7. #7
    Super Member dhiab's Avatar
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    Hello : 1005 and wilmer
    you have one solution
    but (1-x)/(1+x)>= 0
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  8. #8
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    Quote Originally Posted by dhiab View Post
    Hello : 1005 and wilmer
    you have one solution
    but (1-x)/(1+x)>= 0
    Hmmm....isn't all that's required: x <> -1 ?
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