**Explanation of (x^2 - 1)/(x^2)**

To explain the given expression, we need to first substitute the value of x in terms of a radical expression.

**Substituting x**

Given that x = 2√3, we can substitute this value in the expression to get:

(x^2 - 1)/(x^2) = ((2√3)^2 - 1)/(2√3)^2

Simplifying the numerator and denominator, we get:

(x^2 - 1)/(x^2) = (12 - 1)/(4*3)

(x^2 - 1)/(x^2) = 11/12

Therefore, the value of (x^2 - 1)/(x^2) when x = 2√3 is 11/12.

**Understanding the Expression**

The expression (x^2 - 1)/(x^2) can also be written as 1 - 1/x^2. This means that we can think of the expression as the difference between 1 and the reciprocal of x^2.

In the given case, x^2 = (2√3)^2 = 4*3 = 12. Therefore, 1/x^2 = 1/12.

Substituting this value, we get:

(x^2 - 1)/(x^2) = 1 - 1/12

Simplifying, we get:

(x^2 - 1)/(x^2) = 11/12

**Conclusion**

In conclusion, the expression (x^2 - 1)/(x^2) evaluates to 11/12 when x = 2√3. This expression can also be understood as the difference between 1 and the reciprocal of x^2.

X=2+root 3
x^2-1/x^2 can be written as 1-1/x^2
(2+ root 3)^2=4+3+4 root 3
7+ 4 root 3
rationalise it
1/7+ 4 root 3×7-4 root 3/7-4 root 3
7- 4 root 3/1
1-7+ 4 root 3=-6+4 root 3/1