Rearranging an Equation

Date: 05/01/99 at 14:04:22
From: Michael
Subject: Rearranging an equation

Could you please tell me how to rearrange the following equation?

y = (900x)/(2+x)

Date: 05/01/99 at 21:01:56
From: Doctor Peterson
Subject: Re: Rearranging an equation

Hi, Michael.

I'll assume you want to solve for x in terms of y.

The trick is to think of y as a constant; if you aren't confident with 
this sort of thing yet, you might try a practice run with y replaced 
by a number, say 2:

        900x
    2 = -----
        2 + x

How would you solve this for x? Multiply both sides by (2 + x) and 
you'll get

    2(2 + x) = 900x

Now you can distribute the 2:

    4 + x = 900x

Now subtract x from both sides:

    4 = 899x

Finially, divide by 899:

    x = 4/899

Let's do the same thing keeping the y in place:

        900x
    y = -----
        2 + x

Multiply both sides by (2 + x) and you'll get

    y(2 + x) = 900x

Now you can distribute the y:

    2y + yx = 900x

Now subtract yx from both sides (this is where it can be hard to 
remember that y is just a constant, and should be treated like the 
900):

    2y = (900 - y)x

Finially, divide by (900 - y):

    x = 2y/(900 - y)

Now you have x in terms of y. Let's check it:

                     2y
            900 * -------
    900x          900 - y       900 * 2y      1800y
    ----- = ------------- = --------------- = ----- = y
    2 + x           2y      2(900 - y) + 2y   1800
             2 + -------
                 900 - y

Wow - it worked!

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/