Verified answer

Answer:

To simplify the expression:

√2/√6 - √2 - √3/√6 + √2

First, let's simplify each term individually:

√2/√6 can be rationalized by multiplying the numerator and denominator by √6:

(√2/√6) * (√6/√6) = (√12)/6

√2 remains the same.

√3/√6 can also be rationalized by multiplying the numerator and denominator by √6:

(√3/√6) * (√6/√6) = (√18)/6

Now, substituting the simplified terms back into the expression:

(√12)/6 - √2 - (√18)/6 + √2

Combining like terms:

[(√12) - (√18)]/6

To simplify further, we can simplify the square roots:

√12 = √(4 * 3) = 2√3

√18 = √(9 * 2) = 3√2

Substituting these values back into the expression:

[(2√3) - (3√2)]/6

Now we have:

(2√3 - 3√2)/6

This is the simplified form of the given expression.