Question

....... OFER COROANA ........

Answer 1

23)E(x)=(x-3)/(x+3)·[1/(x-3)-1/(x+3)]÷(x+3)^-2
[(1/(x-3)-1/(x+3)]=(x+3-x+3)/(x-3)(x+3)=6/(x-3)(x+3)
(x+3)^-2=1/(x+3)²
⇒E(x)=(x-3)/(x+3)·6/(x-3)(x+3)·(x+3)²=6(am redus termenii asemenea)
a)A={x∈R/E(x) are sens} :x-3≠o⇒x≠3 si x+3≠0⇒x≠-3⇒
A=R/{-3;3}

24) a)E(x)=[2/(x²-1)+1/(x+1)-1/(1-x)]·(x+1/(x-1)
vom amplifica fractiile din paranteza astfel:a 2-a cu (x-1) si a 3-a cu (x+1)⇒
E(x)=[2(x+1)/(x-1)(x+1)]·(x+1)/2
E(x)=(x+1/(x-1) pt.∀x∈R/{-1,1}
c)E(x)=2⇒(x+1)/(x-1)=2⇒(x+1)=2(x-1)⇒x=3
b)pt.x∈N/{-1,1)⇒E(x)=nr.intreg