Simplify the following:
1/(sqrt(2)+sqrt(3))
Multiply numerator and denominator of 1/(sqrt(2)+sqrt(3)) by sqrt(2)-sqrt(3):
(sqrt(2)-sqrt(3))/((sqrt(2)+sqrt(3)) (sqrt(2)-sqrt(3)))
(sqrt(2)+sqrt(3)) (sqrt(2)-sqrt(3)) = sqrt(2) sqrt(2)+sqrt(2) (-sqrt(3))+sqrt(3) sqrt(2)+sqrt(3) (-sqrt(3)) = 2-sqrt(6)+sqrt(6)-3 = -1:
(sqrt(2)-sqrt(3))/(-1)
Multiply numerator and denominator of (sqrt(2)-sqrt(3))/(-1) by -1:
-(sqrt(2)-sqrt(3))
-(sqrt(2)-sqrt(3)) = sqrt(3)-sqrt(2):
Answer: | sqrt(3)-sqrt(2)
