Verified answer

Simplify ( √2 + √3 )(√2 - √3 ) ÷ √3 (√3 - 2√48 )

1) Factor √48 as √4*4*3

2) Write that as 2*2√3

Same as 4√3

Now the expression says

( √2 + √3 )(√2 - √3 ) ÷ √3 (√3 - 8√3 )

2) Multiply ( √2 + √3 )(√2 - √3 )

When you do, you bring back the original binomial (a Difference of Two Squares)

2 - 3

Now the expression says

2 - 3 ÷ √3 (√3 - 8√3 )

3) Clear the parentheses by distributing the √3 coefficient

2 - 3 ÷ 3 - 8*3

Same as 2 - 3 ÷ 3 - 24

4) Compute the numbers

- 1 ÷ - 21

Same as

1 / 21 <-- answer

1/21