Question

$frac{a+2a frac{1}{2} x frac{1}{2} +x }{ax frac{1}{2}+a frac{1}{2} x }$

Answer 1

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