a.4/√7+1/2√7-3/5√7+9/10√7=4√7/7+√7/14-3√7/35+9√7/70=
=(40√7+5√7-6√7+9√7)/70=48√7/70=24√7/35
b.2/(√5+√7)+3/(√7+√10)+4/(√10+√14)=
=2(√5-√7)/(√5+√7)(√5-√7)+3(√7-√10)/(√7+√10)(√7-√10)+
+4(√10-√14)/(√10+√14)(√10-√14)=
=2(√5-√7)/(5-7)+3(√7-√10)/(7-10)+4(√10-√14)/(10-14)=
=2(√5-√7)/(-2)+3(√7-√10)/(-3)+4(√10-√14)/(-4)=
=-√5+√7-√7+√10-√10+√14=
=√14-√5
c.6/(√6+√4)-3/(√5+√6)+8/(√5+√9)=
=6(√6-√4)/(√6+√4)(√6-√4)-3(√5-√6)/(√5+√6)(√5-√6)+
+8(√5-√9)/(√5+√9)(√5-√9)=
=6(√6-√4)/(6-4)-3(√5-√6)/(5-6)+8(√5-√9)/(5-9)=
=6(√6-√4)/2-3(√5-√6)/(-1)+8(√5-√9)/(-4)=
=3√6-3√4+3√5-3√6+2√5-2√9=
=-3√4+5√5-6
d.1/(√2-1)+1/(√2+1)-1/(√3-√2)+1/(√3+√2)=
=(√2+1)/(√2-1)(√2+1)+(√2-1)/(√2+1)(√2-1)-(√3+√2)/(√3-√2)(√3+√2)+
+(√3-√2)/(√3+√2)(√3-√2)=
=(√2+1)/(2-1)+(√2-1)/(2-1)-(√3+√2)/(3-2)+(√3-√2)/(3-2)=
=√2+1+√2-1-√3-√2+√3-√2=
=0
