Va rog ajutati-ma cu acest ex va rog

Răspunsuri la întrebare
Răspuns:
Explicație pas cu pas:
E(x)=[1/(x+2)-1/(x-2)+(x+1)/(x²-4)]:(x²-9)/(x²+x-6)=
[1/(x+2)-1/(x-2)+(x+1)/(x²-4)]·(x²+x-6)/(x²-9)
a) E(x) are sens cand numitorii sunt diferiti de 0.
⇒(x²-4)≠0 ⇒x≠2 si x≠-2
(x²-9)≠0 ⇒x≠3 si x≠-3 ⇒ E(x) are sens pt. x∈R\{-3, -2, 2, 3}
b) E(x)=[1/(x+2)-1/(x-2)+(x+1)/(x²-4)]:(x²-9)/(x²+x-6)=
[1/(x+2)-1/(x-2)+(x+1)/(x²-4)]·(x²+x-6)/(x²-9)=
{[(x-2)-(x+2)+(x+1)]/(x²-4)}·(x²+x-6)/(x²-9)={(x-2-x-2+x+1)/(x²-4)}(x²+x-6)/(x²-9)=[(x-3)/(x²-4)](x²-4+x-2)/(x²-9)=[(x-3)/(x²-4)][(x-2)(x+2)+x-2]/(x²-9)=[(x-3)/(x²-4)][(x-2)(x+2+1)/(x²-9)]= [(x-3)/(x²-4)][(x-2)(x+3)/(x²-9)]=
[(x-3)(x-2)(x+3)]/[(x²-4)(x²-9)]=[(x²-9)(x-2)]/[(x²-4)(x²-9)]= (x-2)/(x²-4)=
(x-2)/(x-2)(x+2)=1/(x+2)
c) E(7)=1/(7+2)=1/9
E(1/4)=1/(1/4+2)=1/(9/4)=4/9
Media geometrica = √[E(7)·E(1/4)]=√(1/9)·(4/9)=√4/81=√(2²/9²)=2/9