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

#### skibum143

1. Homework Statement
solve for x:

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

I need to solve for x.

2. Homework 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?

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#### icystrike

1. Homework Statement
solve for x:

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

I need to solve for x.

2. Homework 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?
Now. cross multiply

#### skibum143

when I do that, I get x = d...

#### Mark44

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?

#### skibum143

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...

#### Mark44

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?

#### skibum143

I get
(n^2*x^2) / (x^2 + h^2) = d^2 / (d^2 + h^2) ]

#### Mark44

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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