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mamaluj [8]
3 years ago
15

HELP WILL GIVE BRAINLESS Which choice is equivalent to the fraction below? (Hint: Rationalize the

Mathematics
1 answer:
Ad libitum [116K]3 years ago
3 0

Answer:

C. \sqrt{x + 2}  -  \sqrt{x}

Step-by-step explanation:

\frac{2}{ \sqrt{x} +  \sqrt{x + 2}  } \\  \\  =   \frac{2}{ (\sqrt{x} +  \sqrt{x + 2})  } \times  \frac{(\sqrt{x}  -   \sqrt{x + 2})}{(\sqrt{x}  -   \sqrt{x + 2})}  \\  \\  =  \frac{2( \sqrt{x}  -  \sqrt{x + 2}) }{ ({ \sqrt{x} )}^{2}  -  {( \sqrt{x + 2} )}^{2} }  \\  \\  = \frac{2( \sqrt{x}  -  \sqrt{x + 2}) }{ x  -  {( x + 2)} }  \\  \\  = \frac{2( \sqrt{x}  -  \sqrt{x + 2}) }{ x  -   x  - 2 } \\  \\  = \frac{2( \sqrt{x}  -  \sqrt{x + 2}) }{  - 2 }  \\  \\  =  - ( \sqrt{x}  -  \sqrt{x + 2})  \\  \\  \frac{2}{ \sqrt{x} +  \sqrt{x + 2}  } =   \purple{ \bold{\sqrt{x + 2}  -  \sqrt{x} }}

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