Answer:
A sqrt(x+2) - sqrt(x)
Step-by-step explanation:
2
--------------
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))
------------------------------
sqrt(x^2) - sqrt(x) sqrt(x+2) + sqrt(x) sqrt(x+2) - sqrt(x+2)^2
2 sqrt(x) - 2 sqrt(x+2)
------------------------------
x - (x+2)
Distribute the minus sign
2 (sqrt(x) - sqrt(x+2))
------------------------------
x - x-2
2 (sqrt(x) - sqrt(x+2))
------------------------------
-2
Cancel the 2 in the top and bottom
(sqrt(x) - sqrt(x+2))
------------------------------
-1
Distribute the -1
sqrt(x+2) - sqrt(x)
