Answer:

(√3-1)/(√3+1)

=[(√3-1)/(√3+1)]×[(√3-1)/(√3-1)]
 =(3+1-2√3)/(3-1)
=(4-2√3)/2
=[2(2-√3)]/2
=2-√3

a-b√3=2-√3

∴the values of a=2 and b=1
So the values of a and b are 2 and 1 respectively.

To simplify the expression, we need to rationalize the denominator. We can do this by multiplying both the numerator and denominator by the conjugate of the denominator, which is sqrt(3) + 1.

[(sqrt(3)-1) / sqrt(3) 1] x [(sqrt(3)+1) / (sqrt(3)+1)]
= [(sqrt(3)(sqrt(3)+1) - 1(sqrt(3)+1)) / (3-1)]
= [(3+sqrt(3) - sqrt(3) - 1) / 2]
= [(2) / 2]
= 1


From the simplified expression, we can see that it is equal to 1. This means that a b sqrt(3) is equal to 0. Therefore, we can conclude that:

a = 0
b = any real number


To find the value of the expression, we first had to simplify it by rationalizing the denominator. We did this by multiplying both the numerator and denominator by the conjugate of the denominator. This allowed us to eliminate the square root in the denominator and simplify the expression.

From the simplified expression, we can see that a b sqrt(3) is equal to 0. This means that a must be 0, since any real number multiplied by 0 is 0. However, b can be any real number, since multiplying it by 0 will still result in 0.

Therefore, the solution to the expression is 1, and the values of a and b are a = 0 and b = any real number.