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I saw a very similar question titled:

"strange behaviour when solving equations symbolically"

The answer basically was it can't do it.

I guess I have been so impressed by Sage so far, that I thought it looked like a simple problem.

I am learning Sage on the Notebook by reworking examples in my old algebra book (starting with page one). Could someone please explain the following behavior and how to solve the original equation?

This equation isn't getting solved:

solve(sqrt(2*x - 5) - sqrt(x - 3) == 1, x)

The output is:

[sqrt(x - 3) == sqrt(2*x - 5) - 1]

But the solution is x == 7 or x == 3

I tried the terms and they are solved:

solve(sqrt(2*x-5) == 1, x)
[x == 3]

solve(sqrt(x-3) == 1 , x)
[x == 4]

Thank you