$\dfrac{\sqrt{x + 1}}{2x + 1} + \dfrac{\sqrt{2x + 1}}{x + 1} = 1 \tag 1$
How can I find the value of $x$ in this question?
2026-02-23 10:45:31.1771843531
Simplification of identity with square roots
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If you want to do this algebraically, isolate one of the square roots on one side of the equation, square both sides, isolate the other square root, square again, simplify and take the numerator. You'll get a polynomial of degree $8$ whose roots can't be expressed in radicals (its Galois group is $S_8$). One of the real roots of that polynomial is the solution.
In practice, numerical methods (e.g. Newton's) are the way to go.