Can x be found for ax^b - x^(b-2) = c in the general form?

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The discussion focuses on solving the equation axb - x(b-2) = c for x, specifically under the constraints that b is an integer where -2 ≤ b ≤ 4. The participants explore the possibility of using infinite fractions or similar methods to find a solution, noting that special cases such as c=0 or a=0 do not contribute to solving the general problem. The complexity of the equation indicates that a closed-form solution is not feasible.

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I have an long equation I managed to simplify to that form, but now I haven't the foggiest on how to solve for x, any help appreciated
 
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Not in a closed form. There might be some way with infinite fractions or similar approaches.
 
Only if ##b\le 4##.
 
... and ##b \geq -2## and an integer.

Or c=0 or a=0, but none of these special cases help with the general problem.
 

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