SOLUTION: i'm having problems solving for specific variables. The problem is x/x+a = b/a, where I need to solve for x.

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Question 53582: i'm having problems solving for specific variables. The problem is
x/x+a = b/a, where I need to solve for x.

Found 2 solutions by rchill, AnlytcPhil:
Answer by rchill(405) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming your equation is x%2F%28x%2Ba%29=b%2Fa. To solve for x, we need to isolate it on one side of the equation -- it doesn't matter which side. In order to that for our equation, we can just use means-extremes method, also known as cross-multiplying, instead of finding the LCD. So, from cross multiplying, we get ax=b%28x%2Ba%29. Simplifying, we get ax=bx%2Bab. Now just divide both sides by a and we get x=%28bx%29%2Fa%2Bb.

Answer by AnlytcPhil(1810) About Me  (Show Source):
You can put this solution on YOUR website!

I'm having problems solving for specific variables. The 
problem is 
x/x+a = b/a, where I need to solve for x. 

                         x       b
                      ------- = ---
                       x + a     a

Cross multiply. I will explain. It is

(Upper left expression) times (lower right expression)

                        equals 

(upper right expression) times (lower left expression.)

Upper left expression = x
Lower right expression = a
Upper right expression = b
Lower left expression = (x + a)

So the next equivalent equation is

                        (x)(a) = (b)(x + a)

Don't need all those parentheses

                            xa =  b(x + a)

Use the distributive principle to remove the
parentheses on the right:

                            xa = bx + ba

Get rid of the x term on the right side by
adding -bx to both sides:

                            xa = bx + ba
                           -bx  -bx
                        -------------------
                       xa - bx =      ba

Factor out x on the left by using the distributive 
principle in reverse

                       x(a - b) = ba

Divide both sides by (a - b)
                           
                      x(a - b)       ba
                      --------- = ---------
                       (a - b)     (a - b)

We can cancel the (a - b)'s on the left

                          1
                      x(a - b)       ba
                      --------- = ---------
                        (a - b)    (a - b)
                          1

So there's just x left on the left

                                     ba
                              x = ---------
                                   (a - b)

To make the answer look better change the ba to ab
(alphabetical order) and drop the parentheses on 
the bottom:

                                     ab
                              x = ---------
                                    a - b

Edwin