Question

1/a+b+x =1/a+1/b+1/x

Answer 1

 1/a+b+x  = 1/a + 1/b + 1/c

1/a+b+x = bx+ax+ab/abx

abx = 3abx + a2x +b2x + a^2b+ab^2

x^2 ( a+b) + x( a^2 + b^2 +2ab ) + ab( a+b) =0

x^2 ( a+b) + x(a+b)2 + a^2b+ ab^2 = 0

D = b^2 - 4ac

= (a+b)4 - 4 ( a+b) ( a^2b+ab^2 ) 

= a^4 + b^4 + 4a3b + 4ab3 + 6a^2b^2 - 4a^3b - 4ab^3 - 8a^2b^2

= a^4 + b^4 - 2a^2b^2

= (a^2 - b^2)2

x = -(a+b)2   (+or -) root of  (a^2-b2)2 / 2(a+b)

 = -a^2 - b^2 -2ab +a^2 -b2/a(a+b)

 = -2b^2 - 2ab/2(a+b)

 = -2b(a+b)/2(a+b) 

 = -b

similarly the other root is -a