Question

Aratati ca e(x pentru orice x apartine R \{-1 1 3} ex 5

Answer 1

Răspuns

Explicație pas cu pas:

x^2 - 9 = (x - 3)(x + 3)

x^2 - 4x + 3 = x^2 - x - 3x + 3 = x(x - 1) - 3(x - 1) = (x- 1)(x - 3)

(x - 3)(x + 3) / (x- 1)(x - 3) = (x + 3) / (x - 1)

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

(x + 3) / (x - 1)  + (x + 2)/(x + 1) - (x^2 + 5x + 2) / (x - 1)(x + 1) =

= (x + 3)(x + 1) / (x - 1)(x + 1)  + (x + 2)(x - 1) / (x - 1)(x + 1) - (x^2 + 5x + 2) / (x - 1)(x + 1) =

= (x^2 + x + 3x + 3 + x^2 - x + 2x - 2 - x^2 - 5x - 2) / (x - 1)(x + 1) =

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

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