Find x (x-b-c)/a + (x-c-a)/b + (x-c-a)/c = 3

Question

(x-b-c)/a + (x-c-a)/b + (x-c-a)/c = 3

Find x

Answer 1

Use a common denominator of abc to rewrite the 3 equations

 

(xbc-b^2c-bc^2)/abc + (xac-c^2a-ca^2)/abc + (xab-abc-ba^2)/abc = 3

 

 

multiply by abc on both sides

 

(xbc-b^2c-bc^2) + (xac-c^2a-ca^2) + (xab-abc-ba^2) = 3abc

 

x(bc+ac+ab) = 3abc +cb^2+bc^2+ac^2+ca^2+abc+ba^2

 

x = (3abc +cb^2+bc^2+ac^2+ca^2+abc+ba^2)/(bc+ac+ab)

 

x = (a^2 (b + c) + b c (b + c) + a c (4 b + c))/(b c + a (b + c))