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Se considera expresia E(x)= [tex] \frac{(x+1)^{2}-4 }{x} : \frac{ x^{2} -x}{ x^{2} } [/tex] , unde x este numar real, x≠0 si x≠1. Determinati numarul real m , m≠0 si m≠1, stiind ca E(m)=5.

Răspuns :

E(x)=[(x+1)²-4]/x : (x²-x)/x²
E(x)=[(x+1)²-4]/x : (x²-x)/x²
E(x)=(x+1-2)(x+1+2)/x · x²/x(x-1)
E(x)=(x+1-2)(x+1+2)/x · x²/x(x-1)
E(x)=(x-1)(x+3) /(x-1)
E(x)=(x+3)
x=m
E(m)=(m+3)=5
m=2