Question

Ce este x/z=0,(6) calculeaza x+z/2x+z

Answer 1

x/z = 0.(6) = 6/9 = 2/3 => x = 2z/3

(x + z)/(2x + z) =

= (2z/3 + z)/(4z/3 + z)

= 5z/7z

= 5/7

Answer 2

$\dfrac{x}{z} = 0,(6) \Rightarrow \dfrac{x}{z} = \dfrac{6}{9} \Rightarrow x = 6 k,\quad z = 9k, ~~ k\in \mathbb{R}^* \\ \\ \dfrac{x+z}{2x+z} = \dfrac{6k+9k}{2\cdot 6k + 9k} = \dfrac{15~\cdot \not{k}}{21~\cdot \not{k}} = \dfrac{15}{21} = \dfrac{5}{7}$