SOLUTION: Solve for a. (a/x)^3 + (b/x) = c

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Question 1208662: Solve for a.

(a/x)^3 + (b/x) = c
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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Solve for a.
(a/x)^3 + (b/x) = c
~~~~~~~~~~~~~~~~~~~ 

You start from

    %28a%2Fx%29%5E3 + b%2Fx = c.


    As your starting equation is written in this form, 
    it is assumed implicitly that x =/=0.


Isolate the term with "a" in the left side

    %28a%2Fx%29%5E3 = c - b%2Fx.


Since left side is the fraction, write right side as a fraction, too

    %28a%2Fx%29%5E3 = %28cx+-+b%29%2Fx.


It is the same as 

    a%5E3%2Fx%5E3 = %28cx-b%29%2Fx.


Multiply both sides by  x%5E3

    a%5E3 = %28x%5E3%2A%28cx-b%29%29%2Fx = x%5E2%2A%28cx-b%29


Now take cube roots of both sides

    a =  root%283%2C+x%5E2%2A%28cx-b%29%29.


It is the desired expression for "a".

Solved.