<s>[INST] Simplest way to solve radical equation $\sqrt{3x+1}-\sqrt{x+4}=1$ I have the following equation:
$$\sqrt{3x+1}-\sqrt{x+4}=1$$
I can get the answer $x=5$ through tedious and long algebraic manipulation with quite a few extraneous solutions. It's not elegant. Is there a simple, straightforward way to solve this equation?
 [/INST] Condition: $x\geq -\frac{1}{3}$.
One has $\sqrt{3x+1} = \sqrt{x+4} + 1$, then $3x+1 = x+4 +1 + 2\sqrt{x+4}$.
So $x-2 = \sqrt{x+4}$. Note that $x \geq 0$.
Then $x^2-4x+4=x+4$, or $x^2-5x = 0$. So $x=5$.
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