Solution:

To simplify the given expression, we need to rationalize the denominator.

Step 1: Rationalizing the denominator

To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator.

Conjugate of the denominator: √3+√2

Multiplying the numerator and denominator by the conjugate of the denominator, we get:

[ (√3 √2-1) ( √3+√2) ] / [(√3-√2) ( √3+√2) ]

Step 2: Simplifying the numerator

Expanding the numerator using the distributive property, we get:

√3 × √3 + √3 × √2 - √2 × √3 - √2 × √2 - 1 × √3 - 1 × √2

Simplifying further, we get:

3 + √6 - √6 - 2 - √3 - √2

3 - 2 - √3 - √2

1 - √3 - √2

Step 3: Simplifying the denominator

Expanding the denominator using the distributive property, we get:

√3 × √3 - √3 × √2 + √2 × √3 - √2 × √2

Simplifying further, we get:

3 - √6 - √6 - 2

1 - 2√6

Step 4: Simplifying the expression

Substituting the simplified numerator and denominator in the expression, we get:

(1 - √3 - √2) / (1 - 2√6)

Thus, the simplified expression is (1 - √3 - √2) / (1 - 2√6).