<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] Because $$\frac{a+b-\sqrt{a^2-b^2}}{\sqrt{a+b}}=\frac{\left(\sqrt{a+b}\right)^2-\sqrt{(a-b)(a+b)}}{\sqrt{a+b}}=\sqrt{a+b}-\sqrt{a-b}$$ 
The domain is $a+b>0$ and $(a-b)(a+b)\geq0,$ which gives $a+b>0$ and $a-b\geq0.$
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