Solution:
To find the value of the expression (x-√126/√42)(x-1/2√3/3), we need to simplify it step by step. Let's break down the given expression into smaller parts and simplify each part individually.

Simplifying the first factor:
Let's simplify the expression x-√126/√42 first.

Step 1: Simplify the square roots
√126 can be simplified as √(9 * 14), which further simplifies to 3√14.
√42 can be simplified as √(6 * 7), which further simplifies to √6√7.

Step 2: Substitute the values of x
Since x = √3, we can substitute the value of x in the expression:
x - √126/√42 becomes √3 - 3√14/√6√7.

Step 3: Rationalize the denominator
To simplify the expression further, we need to rationalize the denominator. We multiply both the numerator and denominator by √6√7 to eliminate the square roots in the denominator.

√3 - 3√14/√6√7 * √6√7/√6√7
= (√3 * √6√7 - 3√14 * √6√7)/(√6√7 * √6√7)
= (√18√42 - 3√84)/(√6√7 * √6√7)
= (√756 - √252)/(√6√7 * √6√7)
= (√756 - √252)/(6√7)

Simplifying the second factor:
Now let's simplify the expression x-1/2√3/3.

Step 1: Simplify the fraction
1/2√3/3 can be simplified as 1/2 * √3/3.
= √3/6
= 1/6√3

Step 2: Substitute the values of x
Since x = √3, we can substitute the value of x in the expression:
x - 1/2√3/3 becomes √3 - 1/6√3.

Simplifying the entire expression:
Now that we have simplified both factors individually, we can multiply them together.

(√3 - 3√14/√6√7)(√3 - 1/6√3)
= (√3 * √3 - √3 * 1/6√3 - 3√14 * √3 + 3√14 * 1/6√3)/(√6√7 * √6√7)
= (3 - 1/6 - 3√42 + √14/2√2)/(6√7)
= (18 - 1 - 18√42 + 3√14)/(12√7)
= (17 - 18√42 + 3√14)/(12√7)

Therefore, the value of the expression (x-√126