Explicație pas cu pas:

x≠0

[tex]\dfrac{1}{x} < 1 \iff 1 - \dfrac{1}{x} > 0 \\ \dfrac{x - 1}{x} > 0[/tex]

x - 1 = 0 => x = 1

pentru

x < 0 => x - 1 < 0

[tex]\implies \dfrac{x - 1}{x} > 0[/tex]

0 < x < 1 => x - 1 < 0

[tex]\implies \dfrac{x - 1}{x} < 0[/tex]

x > 1 => x - 1 > 0

[tex]\implies \dfrac{x - 1}{x} > 0[/tex]

=> x ∈ (-∞; 0) ∪ (1; +∞)