Calculer et donner le le résultat sous la forme d'une fraction la plus simple possible

Bonjour Rbart857

[tex]A=\dfrac{1-2(\dfrac{2}{3}-1)^2}{\dfrac{5}{3}+\dfrac{1}{3}:\dfrac{1}{3^2}} \\\\\\A=\dfrac{1-2(\dfrac{2}{3}-\dfrac{3}{3})^2}{\dfrac{5}{3}+\dfrac{1}{3}:\dfrac{1}{9}} \\\\\\A=\dfrac{1-2(-\dfrac{1}{3})^2}{\dfrac{5}{3}+\dfrac{1}{3}\times9} [/tex]

[tex]\\\\\\A=\dfrac{1-2\times\dfrac{1}{9}}{\dfrac{5}{3}+\dfrac{9}{3}} \\\\\\A=\dfrac{1-\dfrac{2}{9}}{\dfrac{14}{3}} \\\\\\A=\dfrac{\dfrac{9}{9}-\dfrac{2}{9}}{\dfrac{14}{3}} [/tex]

[tex]\\\\\\A=\dfrac{\dfrac{7}{9}}{\dfrac{14}{3}} \\\\\\A=\dfrac{7}{9}\times\dfrac{3}{14}}\\\\A=\dfrac{1}{9}\times\dfrac{3}{2}}\\\\A=\dfrac{1}{3}\times\dfrac{1}{2}}\\\\\boxed{A=\dfrac{1}{6}}[/tex]