Question

Skróć ułamek, podaj konieczne założenia:
x³-1/2x²-2

Answer 1

(x³ - 1)/(2x² - 2)

D : 2x² - 2 ≠ 0 /: 2

x² - 1 ≠0

(x - 1)(x + 1) ≠ 0

x - 1 ≠ 0 ∧ x + 1 ≠ 0

x ≠ 1 ∧ x ≠ - 1

D : x ∈ R \ { - 1, 1 }

x³ - 1 = (x - 1)(x² + x + 1)

(x³ - 1)/(2x² - 2) = (x - 1)(x² + x + 1)/ 2(x² - 1) =

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

= 0,5(x² + x + 1)/(x + 1)

Answer 2

Założenie:
2x²-2≠0
2(x²-1)≠0
2(x-1)(x+1)≠0
x≠1 i x≠-1


x³-1/2x²-2 = (x-1)(x²+x+1)/2(x-1)(x+1)=(x²+x+1)/2(x+1)