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

A:
`√(x + 2) - √(x)`

^.^

- Amanda

Answer 2

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.