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:

A sqrt(x+2) - sqrt(x)

Step-by-step explanation:

2

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sqrt(x) + sqrt(x+2)

Multiply top and bottom by sqrt(x) - sqrt(x+2)

2                              sqrt(x) - sqrt(x+2)

------------------------ * --------------------------

sqrt(x) + sqrt(x+2)   sqrt(x) - sqrt(x+2)

FOIL the denominator

2 (sqrt(x) -  sqrt(x+2))

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sqrt(x^2) - sqrt(x) sqrt(x+2) + sqrt(x) sqrt(x+2) - sqrt(x+2)^2

2 sqrt(x) - 2 sqrt(x+2)

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x - (x+2)

Distribute the minus sign

2 (sqrt(x) -  sqrt(x+2))

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x - x-2

2 (sqrt(x) -  sqrt(x+2))

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-2

Cancel the 2 in the top and bottom

(sqrt(x) -  sqrt(x+2))

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-1

Distribute the -1

sqrt(x+2) - sqrt(x)