Explanation:

To find the value of a and b in the expression √3 - 1/√3 = a - b√3, we need to simplify the expression on the left side of the equation.

Step 1: Rationalize the denominator

The expression 1/√3 can be simplified by rationalizing the denominator. To do this, we multiply both the numerator and denominator by √3:

1/√3 = (1/√3) * (√3/√3) = √3/3

Therefore, the expression becomes:

√3 - √3/3 = a - b√3

Step 2: Combine like terms

The expression √3 and -√3/3 are like terms. To combine them, we need a common denominator. The common denominator is 3, so we multiply √3 by 3/3:

√3 - √3/3 = 3√3/3 - √3/3 = (3√3 - √3)/3 = 2√3/3

Now the expression becomes:

2√3/3 = a - b√3

Step 3: Equate the coefficients

In the equation 2√3/3 = a - b√3, the left side represents a fraction with a coefficient of 2/3√3. To equate the coefficients, we compare the numerator and denominator separately:

Numerator:
2√3 = a (since the coefficient of √3 on the right side is a)

Denominator:
3 = -b (since the coefficient of √3 on the right side is -b)

Therefore, we have:
a = 2√3
b = -3

Conclusion:

The value of a is 2√3 and the value of b is -3.