3 - √3

√6

you need to have a common denominator, so let's make √3 into a fraction of something over √6. So let's multiply the √3 by (√6/√6). You can always multiply something by one, since it doesn't change its value.

3 - √3√6

√6 √6

now we can combine the numerator over the common denominator

3 - √3√6

√6

this is now a ratio. but let's try to simply it further by multiplying top and bottom by √6

3√6 - √3√6√6

√6√6

3√6 - 6√3

6

√6 - 2√3

2

√6

you need to have a common denominator, so let's make √3 into a fraction of something over √6. So let's multiply the √3 by (√6/√6). You can always multiply something by one, since it doesn't change its value.

3 - √3√6

√6 √6

now we can combine the numerator over the common denominator

3 - √3√6

√6

this is now a ratio. but let's try to simply it further by multiplying top and bottom by √6

3√6 - √3√6√6

√6√6

3√6 - 6√3

6

√6 - 2√3

2