Question

Which choice is equivalent to the fraction below when x is greater than or equal to 2?

Answer 1

D D D D D D D D D D D D DD D D D D D DD D D D D

Answer 2

D. 2(√{x} + √{x - 2})

Explanation:

As hinted in the question, we have to simplify the denominator.

To understand it easier, let's imagine we have x - y in the denominator. If we multiply it with x + y we'll get x² - y², right? Check the next line:

(x - y) (x + y) = x² + xy -xy - y² = x² - y²

If we have the square of those nasty square roots, it will be much simpler to deal with. So, let's multiply the initial fraction using x+y, but with the real values:

`(4)/(√(x) - √(x - 2) ) * (√(x) + √(x - 2))/(√(x) - √(x - 2)) = (4(√(x) + √(x - 2)))/((√(x) )^(2) - (√(x - 2) )^(2) )`

Then we simplify:

`(4(√(x) + √(x - 2)))/((√(x) )^(2) - (√(x - 2) )^(2) ) = (4(√(x) + √(x - 2)))/((x) - (x - 2) ) = (4(√(x) + √(x - 2)))/( 2 ) = 2(√(x) + √(x - 2))`

Answer is D. 2(√{x} + √{x - 2})