Question

dau coroana si 30 pct

Answer 1

Răspuns:

Explicație pas cu pas:

a)

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

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

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

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

__________

x^3 - x = x(x^2 - 1) = x(x - 1)(x + 1)

__________

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

b)

2/(x + 2) ∈ Z ⇒ x + 2 ∈ {-2, -1, 1, 2} ⇒ x ∈ {-4, -3, -1, 0}

am avut si conditia ca x ∈ R \ {-2, -1, 0, 1}

⇒ x = {-4, -3}