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Thread: Can someone help me solve this equation?

  1. #1
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    Can someone help me solve this equation?

    Equation: x = ( y+z ) / ( y-z )

    We only know x and z, I try to solve:

    x ( y-z) = y+z
    xy - xz = y + z
    xy - y = z + xz

    But this method not resolve it.

    Can you help me?

    Sorry for my english but I am not english

    Thanks!
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  2. #2
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    Re: Can someone help me solve this equation?

    $x = \dfrac{y+z}{y-z}$

    solving for $y$

    $(y-z)x = y+z$

    $x y - x z = y + z$

    $xy - y = xz + z$

    $(x-1)y = x(z+1)$

    $y = \dfrac{x(z+1)}{x-1}$
    Thanks from luisgzafra
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  3. #3
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    Re: Can someone help me solve this equation?

    Quote Originally Posted by romsek View Post
    $x = \dfrac{y+z}{y-z}$

    solving for $y$

    $(y-z)x = y+z$

    $x y - x z = y + z$

    $xy - y = xz + z$

    $(x-1)y = x(z+1)$

    $y = \dfrac{x(z+1)}{x-1}$
    I should add that the step


    $(x-1)y = x(z+1) \to y = \dfrac{x(z+1)}{x-1}$

    is valid only if $x \neq 1$
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  4. #4
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    Re: Can someone help me solve this equation?

    Quote Originally Posted by romsek View Post
    $xy - y = xz + z$

    $(x-1)y = x(z+1)$
    Typo: = z(x+1)
    To the corner for (x + z) minutes...
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