Bonjour, Je me retrouve coincé devant une énigme dans un DM de Maths... Merci de votre aide

Bonjour,

[tex]\dfrac{41}{17+\dfrac{47}{4-\dfrac{51}{x}}}=\dfrac{2009}{2008}\\\\\\\dfrac{49\times41}{49(17+\dfrac{47}{4-\dfrac{51}{x}})}=\dfrac{2009}{2008}\\\\\dfrac{2009}{49(17+\dfrac{47}{4-\dfrac{51}{x}})}=\dfrac{2009}{2008}\\\\\\49(17+\dfrac{47}{4-\dfrac{51}{x}})=2008[/tex]


[tex]17+\dfrac{47}{4-\dfrac{51}{x}}=\dfrac{2008}{49}\\\\\\\dfrac{47}{4-\dfrac{51}{x}}=\dfrac{2008}{49}-17\\\\\\\dfrac{47}{4-\dfrac{51}{x}}=\dfrac{2008}{49}-\dfrac{833}{17}\\\\\\\dfrac{47}{4-\dfrac{51}{x}}=\dfrac{1175}{49}[/tex]



[tex]\dfrac{25\times47}{25(4-\dfrac{51}{x})}=\dfrac{1175}{49}\\\\\\\dfrac{1175}{25(4-\dfrac{51}{x})}=\dfrac{1175}{49}\\\\\\25(4-\dfrac{51}{x})=49\\\\100-\dfrac{1275}{x}=49\\\\-\dfrac{1275}{x}=49-100\\\\-\dfrac{1275}{x}=-51[/tex]

[tex]\dfrac{1275}{x}=51\\\\51x=1275\\\\x=\dfrac{1275}{51}\\\\x=25[/tex]