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Solving for a variable when the square root of a formula is in the denominator

  1. Mar 17, 2010 #1
    1. The problem statement, all variables and given/known data
    solve for x:

    [ x / sqrt(x^2 + h^2) ] = [ d / sqrt(d^2 + h^2) ]

    I need to solve for x.

    2. Relevant equations
    sq rt * sq rt = what is inside the square root
    square both sides of an equation

    3. The attempt at a solution

    Can anyone help me remember how to get rid of the sqrt of x on the bottom of the left hand side? If I multiply by the sq rt of the ( ) I will have to do it on the other side, so I will still have the sq rt.

    If I square both sides of the equation, I think that I would get: x^2 / (x^2 + h^2) = d^2 / (d^2 + h^2) Is that right? If so, I don't know where to go from there to solve for x?
  2. jcsd
  3. Mar 18, 2010 #2
    Now. cross multiply
  4. Mar 18, 2010 #3
    when I do that, I get x = d...
  5. Mar 18, 2010 #4


    Staff: Mentor

    I got two solutions, one of which turned out to be extraneous. Did you get two solutions before deciding to discard one of them?
  6. Mar 18, 2010 #5
    I'm so sorry - I forgot the n in the right side of the equation, it should read like this:

    n * [ x / sqrt(x^2 + h^2) ] = [ d / sqrt(d^2 + h^2) ]

    when I solved this, I got x = d/n

    But i only got that one equation...
  7. Mar 18, 2010 #6


    Staff: Mentor

    You're showing n on the left side of the equation.

    I don't get x = d/n at all. When you square both sides of your equation what do you get?
  8. Mar 18, 2010 #7
    I get
    (n^2*x^2) / (x^2 + h^2) = d^2 / (d^2 + h^2) ]
  9. Mar 18, 2010 #8


    Staff: Mentor

    Now multiply both sides by (x^2 + h^2)(d^2 + h^2). After doing that, move terms around so that all the terms with x in them are on one side, and all the rest are on the other side. You should be able to factor x^2 out as a preliminary step to isolating it.
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