1/(5√2+7)=1·(5√2-7)/(5√2+7)(5√2-7)=(5√2-7)/(5²√2²-7²)=(5√2-7)/(25·2-49)=
(5√2-7)/51
√5-√3/√5+√3=(√5-√3)(√5-√3)/(√5+√3)(√5-√3)=(√5-√3)²/√5²-√3²=(5-2√5·√3+3)/(5-3)=(8-√15)/2
(2√7+√5)/(2√7-√5)=(2√7+√5)(2√7+√5)/(2√7-√5)(2√7+√5)=(2√7+√5)²/((2√7)²-√5²)=((2√7)²-2·2√7·√5+√5²)/(4·7-5)=(28-4√35+5)/23=(33-4√35)/23
14/(3√3-2√5)=14·(3√3+2√5)/(3√3-2√5)(3√3+2√5)=(42√3+28√5)/((3√3)²-(2√5)²)=(42√3+28√5)/(9·3-4·5)=(42√3+28√5)/7
3/4√3-3√5=3·(4√3+3√5)/(4√3-3√5)(4√3+3√5)=(12√3+9√5)/((4√3)²-(3√5)²)=(12√3+9√5)/16·3-9·5=(12√3+9√5)/3