Question

E(x)=xla patrat -9 /(x-1)la patrat-4
a) Aratati ca E(2) + E(-1) apartine lui N
b)Simplificati fractia
c)Determinati valorile intregi ale lui x pentru carw E(x) apartine lui Z

Answer 1

E(x)=(x-3)(x+3)/[x²-2x+1-4]=
E(x)=(x-3)(x+3)/(x²-2x-3)
a)
E(2)+E(-1)=[(4-9)/(2-1)²-4]+[(1-9)/(-1-1)²-4]=(-3/-3)+(-8/0)=1∈N
b) E(x)=(x-3)(x+3)/[x²-2x+1-4]=
E(x)=(x-3)(x+3)/(x²-2x-3)
E(x)=(x-3)(x+3)/(x+1)(x-3)  simplif. cu x-3
E(x)=(x+3)/(x+1)
c)
cond x≠-1
x+3=0
x=-3