Stuck with this non-trivial algebra, solving for x

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The discussion centers on solving a non-trivial algebraic equation for the variable x, with participants attempting to simplify the expression. One user suggests treating the equation as a quadratic, while another emphasizes the importance of checking solutions against the original equation. Key insights include the recommendation to multiply through by a common denominator to eliminate fractions and the suggestion to verify potential solutions by substituting them back into the equation. The final expression discussed includes terms such as c^2m^2 and a^2b^2.

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Homework Statement


I am trying to solve for x in this equation:
upload_2016-11-5_20-20-12.png


Homework Equations

The Attempt at a Solution


I tried solving it like a quadratic equation.
This is the most simplified I could get it.
upload_2016-11-5_20-18-4.png

Can someone please help me find a simpler expression
 
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Cocoleia said:

Homework Statement


I am trying to solve for x in this equation:
View attachment 108531

Homework Equations

The Attempt at a Solution


I tried solving it like a quadratic equation.
This is the most simplified I could get it.
View attachment 108529
Can someone please help me find a simpler expression
Can you please show all of your work and intermediate steps? Thanks. :smile:
 
Cocoleia said:

Homework Statement


I am trying to solve for x in this equation:
View attachment 108531

Homework Equations

The Attempt at a Solution


I tried solving it like a quadratic equation.
This is the most simplified I could get it.
View attachment 108529
Can someone please help me find a simpler expression

Maybe there isn't a simpler expression. Not all simple-looking problems have simple-looking solutions. Anyway, I get a different answer.
 
Last edited:
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A useful habit is to check whether a simple solution to the one expression is also a solution to the other. Your original has the solution x=a=c. That does not appear to be a solution of your final expression.
 
berkeman said:
Can you please show all of your work and intermediate steps? Thanks. :smile:
upload_2016-11-6_11-6-28.png

and then i just simplified to my final answer
 
Third step, shouldn't it be ##\frac{c^2m^2}{b^2}## instead of ##c^2m^2##?
 
Cocoleia said:
and then i just simplified to my final answer

I would have multiplied through the first equation by ##a^2b^2## to get rid of the fractions.
 
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Cocoleia said:
View attachment 108557
and then i just simplified to my final answer
Did you read post #4? You can make further use of this by plugging in the simple solution at various points in your working to see at what point it ceases to be a solution.
 

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