Question

Se considera expresia E(x)= ( x-2 supra x²-4 ori 5x+10 supra x-3 +1 )ori x-3 supra x+2,unde x  este numar real,x≠-2,x≠2 si x≠3.Aratati ca E(x)=1 pentru orice x numar real x≠-2,x≠2 si x≠3

Answer 1

E(x)= [(x - 2) / (x-2)(x+2) × 5(x+2) / (x-3) +1] ×(x-3)/(x+2) =[ 5 / (x-3) +1]·(x-3/(x+2)] =
= (5+x-3)/(x-3) × (x-3)/(x+2) = (x+2)/(x-3) ×(x-3)/(x+2) = 1