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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

Which choice is equivalent to the fraction below? (Hint: Rationalize the denominator-example-1
User Pjohansson
by
9.0k points

2 Answers

7 votes

Answer:

A:
√(x + 2) - √(x)

^.^

- Amanda

User JimiSweden
by
8.4k points
6 votes

Answer:

Option A.

Explanation:

The given fraction
(2)/(√(x)√(x+2)) is to be simplified.

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


(2(√(x)-√(x+2)))/((√(x)+√(x+2))(√(x)-√(x+2)))

=
(2(√(x)-√(x+2)))/((√(x))^(2)-(√(x+2))^(2) )

[ Since ( a+b) (a-b) = a² - b² ]


(2(√(x)-√(x+2)))/(x-(x+2))=((2√(x)-√(x+2)))/((-2))

=
-(√(x)-√(x+2)=√(x+2)-√(x)

Option A. is the answer.

User WebStuff
by
7.2k points

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