Answer:
Option A.
Step-by-step explanation:
The given fraction [tex]\frac{2}{\sqrt{x}\sqrt{x+2}}[/tex] is to be simplified.
For the simplification of the given fraction we will rationalize the denominator. By multiplying [tex](\sqrt{x}\sqrt{x+2})[/tex] in numerator as well as denominator both, denominator can be rationalized.
[tex]\frac{2(\sqrt{x}-\sqrt{x+2})}{(\sqrt{x}+\sqrt{x+2})(\sqrt{x}-\sqrt{x+2})}[/tex]
= [tex]\frac{2(\sqrt{x}-\sqrt{x+2})}{(\sqrt{x})^{2}-(\sqrt{x+2})^{2} }[/tex]
[ Since ( a+b) (a-b) = a² - b² ]
[tex]\frac{2(\sqrt{x}-\sqrt{x+2)}}{x-(x+2)}=\frac{(2\sqrt{x}-\sqrt{x+2)}}{(-2)}[/tex]
= [tex]-(\sqrt{x}-\sqrt{x+2}=\sqrt{x+2}-\sqrt{x}[/tex]
Option A. is the answer.
