Let's simplify the expression (sqrt(3))/(sqrt(2) + 1) and see if it equals sqrt(2) - 1.
To eliminate the square roots in the denominator, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is (sqrt(2) - 1):
(sqrt(3))/(sqrt(2) + 1) * (sqrt(2) - 1)/(sqrt(2) - 1)
Multiplying the numerators and denominators gives:
(sqrt(3) * (sqrt(2) - 1)) / ((sqrt(2) + 1) * (sqrt(2) - 1))
Simplifying the expression further:
(sqrt(3) * sqrt(2) - sqrt(3)) / (sqrt(2)^2 - 1^2)
(sqrt(6) - sqrt(3)) / (2 - 1)
(sqrt(6) - sqrt(3)) / 1
sqrt(6) - sqrt(3)
So, the simplified expression is sqrt(6) - sqrt(3), which is not equal to sqrt(2) - 1. Therefore, the given equation is incorrect.
