<s>[INST] Simplify $\frac{a+b-\sqrt{a^2-b^2}}{\sqrt{a+b}}$ I have to simplify the following expression:
$A =\frac{a+b-\sqrt{a^2-b^2}}{\sqrt{a+b}}$

Answer: $\sqrt{a+b}-\sqrt{a-b}$

I am trying to find the constraints of $a$ and $b$. I think that $a^2-b^2 \ge 0$ and $a+b \ge 0$. How can I simplify them? (the inequalities)
 [/INST] You can write $$\frac{(a+b)^2-(a^2-b^2)}{\sqrt{a+b}(a+b+\sqrt{a^2+b^2})}$$
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