SOLUTION: solve : (ln(1+4/x)) ^2 +(ln(1-4/(x+4)))^2 =2(ln((3-x)/(x-1)))^2

Question 1109882: solve : (ln(1+4/x)) ^2 +(ln(1-4/(x+4)))^2 =2(ln((3-x)/(x-1)))^2
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The equation has a few restrictions, but we can worry about it later,
as we may have to get rid of some extraneous solutions, anyway.
For now, we will assume , , etc.

If both logarithms have the same sign (both positive or both negative,

<-->

.
Otherwise,

<-->

.

And we trudge on.

For ,
, , , , , and are all positive,
so it looks like a valid solution, and it verifies.
For , ,
so does not exist/is undefined,
so we know is not a solution.
I do not have to try to verify that.

For ,
, , , , , and are all positive,
so it looks like a valid solution, and it verifies.
For , ,
so does not exist/is undefined,
so we know is not a solution.
I do not have to try to verify that.

HOW WE VERIFY:
For

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