Question

Exercitiul 5) E(x)=?
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Answer 1

Răspuns:

Explicație pas cu pas:

x/(x^2 + x) = 1/(x + 1)

________

x/(x - 1) - x/(x + 1) = [x(x + 1) - x(x - 1)]/(x - 1)(x + 1)

= (x^2 + x - x^2 + x)/(x - 1)(x + 1) = 2x/(x - 1)(x + 1)

________

2x/(x - 1)(x + 1) : 2x/(x - 1) = 2x/(x - 1)(x + 1) * (x - 1)/2x = 1/(x + 1)

_________

E(x) = 1/(x + 1) - 1/(x + 1) = 0

Answer 2

Răspuns:

Explicație pas cu pas:

E (x)=x/x(x+1)-(x²+x-x²+x)/(x-1)(x+1)×(x-1)/2x=1/(x+1)-(2x)/(x+1)×1/2x=

=1/(x+1)-1/(x+1)=0

x≠±1  x≠0