Question

Se x = 0,121212...,o valor numerico da expressao \frac{x+\frac{1}{x}-1}{x^{2}+\frac{1}{x}}

Answer 1

Dízima periódica

x = 0,121212 (x100)
100x = 12,121212
100x = 12 + 0,121212
100x = 12 + x
100x - x = 12
99x = 12
x = 12/99(simplifica por 3)
x = 4/33