Answer 1

$\frac{a+2a^{\frac{1}{2}}x^{\frac{1}{2}}+x}{ax^{\frac{1}{2}}+a^{\frac{1}{2}}x}=\frac{a+2\sqrt{ax}+x}{a\sqrt{x}+\sqrt{a}x}=\frac{(\sqrt{a}+\sqrt{x})^2}{\sqrt{ax}(\sqrt{a}+\sqrt{x})}=\frac{\sqrt{a}+\sqrt{x}}{\sqrt{ax}}$

Answer 2

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