1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook