A) 23/(8+3√2) =23*(8 - 3√2) / (8+3√2)(8 -3√2) =23(8 -3√2) /(64 -9*2) =23(8 -3√2) /46 =(8 -3√2)/2
b) (5 -√m)/(5+√m) =(5 -√m)*(5 -√m) /(5+√m)(5 -√m) =(5 -√m)^2 /(25 -m) =(25 -10√m +m) /(25 -m)
в) (a√c +c√a) /√ac =(a√c +c√a)*√ac /(√ac*√ac) =(a√c*√ac +c√a*√ac) /ac =(a√(c*ac) +c√(a*ac)) /ac =(ac√a +ac√c) /ac =ac(√a +√c) /ac =√a +√c
г) =(x -3√x +9)*(√x +3) /(√x -3)(√x +3) =((√x)^3 +27) /(x -9) =(x√x +27) /(x -9)