Question

Which choice is equivalent to the fraction below? (Hint: Rationalize the denominator and simplify.) I NEED HELP HELP PLEASE PLEASE HELP HELP PLEASE HELP ME PLEASE PLEASE HELP PLEASE PLEASE ASAP PLEASE PLEASE THANK

Answer 1

Answer:

Option A.

Step-by-step explanation:

The given fraction $\frac{2}{\sqrt{x}\sqrt{x+2}}$ is to be simplified.

For the simplification of the given fraction we will rationalize the denominator. By multiplying $(\sqrt{x}\sqrt{x+2})$ in numerator as well as denominator both, denominator can be rationalized.

$\frac{2(\sqrt{x}-\sqrt{x+2})}{(\sqrt{x}+\sqrt{x+2})(\sqrt{x}-\sqrt{x+2})}$

= $\frac{2(\sqrt{x}-\sqrt{x+2})}{(\sqrt{x})^{2}-(\sqrt{x+2})^{2} }$

[ Since ( a+b) (a-b) = a² - b² ]

$\frac{2(\sqrt{x}-\sqrt{x+2)}}{x-(x+2)}=\frac{(2\sqrt{x}-\sqrt{x+2)}}{(-2)}$

= $-(\sqrt{x}-\sqrt{x+2}=\sqrt{x+2}-\sqrt{x}$

Option A. is the answer.

Answer 2

Answer:

A: $\sqrt{x + 2} - \sqrt{x}$

^.^

- Amanda