Cho 2a+b+c+d/a=a+2b+c+d/b=a+b+2c+d/c=a+b+c+2d/d Tính M= a+b/c+d + b+c/d+a + c+d/a+b + d+a/b+c Giúp em voi ạ. em can gap

$\text{Ta có:}$ `(2a+b+c+d)/a=(a+2b+c+d)/b = (a+b+2c+d)/c = (a+b+c+2d)/d`

`⇒ (2a+b+c+d)/a – 1=(a+2b+c+d)/b – 1 = (a+b+2c+d)/c – 1= (a+b+c+2d)/d – 1`

`⇒ (a+b+c+d)/a = (a+b+c+d)/b = (a+b+c+d)/c = (a+b+c+d)/d (1)`

`TH1: a + b + c + d \ne 0`

$\text{Từ (1)}$ `⇒ a=b=c=d`

`M = (a+b)/(c+d) + (b+c)/(d+a) + (c+d)/(a+b) + (d+a)/(b+c)`

`= (2a)/(2a) + (2b)/(2b) + (2c)/(2c) + (2d)/(2d)`

`= 1 + 1 + 1 + 1 = 4`

`TH2: a + b + c + d = 0`

`⇒ a + b = -(c + d)`

     `b + c = -(a + d)`

     `c+d = -(a + b)`

     `d + a = -(b + c)`

`M = (a+b)/(c+d) + (b+c)/(d+a) + (c+d)/(a+b) + (d+a)/(b+c)`

`=(-(c+d))/(c+d) + (-(a+d))/(d+a)+(-(a+b))/(a+b)+(-(b+c))/(b+c)`

` = -1 + (-1) + (-1) + (-1) = -4`