aider moi svp pour l enigme

Bonsoir,

[tex]A=1+\dfrac{1+\dfrac{1}{1-\dfrac{1}{5}}}{1-\dfrac{1}{1+\dfrac{1}{5}}}\\\\A=1+\dfrac{1+\dfrac{1}{\dfrac{5}{5}-\dfrac{1}{5}}}{1-\dfrac{1}{\dfrac{5}{5}+\dfrac{1}{5}}}[/tex]

[tex]A=1+\dfrac{1+\dfrac{1}{\dfrac{4}{5}}}{1-\dfrac{1}{\dfrac{6}{5}}}\\\\A=1+\dfrac{1+1\times\dfrac{5}{4}}{1-1\times\dfrac{5}{6}}\\\\A=1+\dfrac{1+\dfrac{5}{4}}{1-\dfrac{5}{6}}[/tex]

[tex]A=1+\dfrac{\dfrac{4}{4}+\dfrac{5}{4}}{\dfrac{6}{6}-\dfrac{5}{6}}\\\\\\A=1+\dfrac{\dfrac{9}{4}}{\dfrac{1}{6}}\\\\\\A=1+\dfrac{9}{4}\times\dfrac{6}{1}}\\\\\\A=1+\dfrac{54}{4}[/tex]

[tex]\\\\\\A=1+\dfrac{27}{2} \\\\\\A=\dfrac{2}{2}+\dfrac{27}{2}\\\\\\\boxed{A=\dfrac{29}{2}}[/tex]