Stuck with this non-trivial algebra, solving for x

[Cocoleia]

Homework Statement

I am trying to solve for x in this equation:

Homework Equations

The Attempt at a Solution

I tried solving it like a quadratic equation.
This is the most simplified I could get it.

Can someone please help me find a simpler expression

 

[berkeman]

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.

 

[Ray Vickson]

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.

 

[haruspex]

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.

 

[Cocoleia]

Can you please show all of your work and intermediate steps? Thanks.

and then i just simplified to my final answer

 

[micromass]

Third step, shouldn't it be $\frac{c^2m^2}{b^2}$ instead of $c^2m^2$?

 

[PeroK]

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.

 

[haruspex]

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.