( √(12+6√3) - √(11-6√2) ) /(√2 -√3) + √24 =
( (3+√3) -(3-√2) ) / (√2 -√3) + √24 = - (√3 +√2) /(√3 -√2) +2√6 =
= - (√3 +√2)(√3 +√2( /(√3 -√2)(√3 +√2) +2√6 = -(√3+√2)² / ((√3)² -(√2)²) +2√6 =
-((√3)²+2√3*√2 +(√2)² )/ (3-2) +2√6 =-(3+2√6 +2) +2√6 = -5 -2√6 +2√6 = - 5.
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√(12+6√3) =√(9+2*3*√3 +3) =√(3² +2*3*√3+(√3)²) = √(3+√3)² =3+√3.
√(11-6√2) = √(9 -2*3*√2 +2) = √(3² -2*3*√2 +(√2)² ) = √(3-√2)² =3 -√2 .
числитель : √(12+6√3) -√(11-6√2) =(3+√3) -(3 -√2) =√3+√2 .