Răspuns:
Explicație pas cu pas:
a) 24/√3+30/5√3-42/7√3+36/√3=
24/√3+5·6/5√3-7·6/7√3+36/√3=
24/√3+6/√3-3/√3+36/√3=
24√3/(√3·√3)+36√3/(√3·√3)=
24√3/3+36√3/3=
8√3+12√3=20√3
b) 16/(2-√3)+12/(√3+1)-6/(2√3-3)-8/(3√3+5)=
16(2+√3)/(2-√3)(2+√3)+12(√3-1)/(√3+1)(√3-1)-6(2√3+3)/(2√3-3)(2√3+3)- 8(3√3-5)/(3√3+5)(3√3-5)=
16(2+√3)/(2²-√3²)+12(√3-1)/(√3²-1²)-6(2√3+3)/(2²√3²-3²)-8(3√3-5)/ (3²√3²-5²)=
16(2+√3)/(4-3)+12(√3-1)/(3-1)-6(2√3+3)/(12-9)-8(3√3-5)/(27-25)=
16(2+√3)/1+12(√3-1)/2-6(2√3+3)/3-8(3√3-5)/2=
16(2+√3)+6(√3-1)-2(2√3+3)-4(3√3-5)=
32+16√3+6√3-6-4√3-6-12√3+20=40+6√3
