7. (10√3+√108-3√27)*(√147)⁻¹=(10√3+√(36*3)-3√(9*3))/√(49*3)=
=(10√3+6√3-9√3)/7√3=(7√3)/(7√3)=1.
8. 9/(7-4√3)=9*(7+4√3)/((7-4√3)*(7+4√3))=9*(7+4√3)/(7²-(4√3)²)=
=9*(7+4√3)/(49-48)=9*(7+4√3)/1=9*(7+4√3).
9. √(3-√7)²+√(2-√7)²=|3-√7|+|2-√7|=3-√7+√7-2=1.
10. (b-3)/(b-2*√3*b+3)=(b-3)/((√b)²-2*√(3*b)+(√3)²)=
=(√b-√3)*(√b+√3)/(√b-√3)²=(√b+√3)/(√b-√3);