Спростити вираз 1/(sqr2 +sqr3)^2

Question

Спростити вираз 1/(sqr2 +sqr3)^2

Answer 1

1/(√2+√3)²=1/(2+2√(2*3)+3)=1/(5+2√6)=(5-2√6)/((5+2√6)(5-2√6))=
=(5-2√6)/(5²-(2√6)²)=(5-2√6)/(25-24)=5-2√6.