`(a+b-c)/(a+b)=(b+c-a)/(b+c)=(c+a-b)/(c+a), a+b+c!=0` find relation

If (a+b-c)/(a+ b) =(b+c-a)/(b+c) = (c+a-b)/(c+a) and a+b+cne 0, then prove that a = b = c.

If (b + c) (y + z) - ax = b - c, (c + a) (z + x) - by = c - a and (a + b) (x + y) - cz = a - b , where a + b + c ne 0, then x is equal to a) (c + b)/(a + b + c) b) (c - b)/(a + b + c) c) (a - b)/(a + b + c) d) (a + b)/(a + b + c)

Show that (a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a) =0

If ={a,b,c} and R={(a,a),(a,b),(b,c),(b,b),(c,c),(c,a)} is a binary relation on A, then one of the following is correct?

|(a - b, b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c)|=0

Show that: (a-b)(a+b)+ (b-c) (b+c) +(c-a) (c+a) =0

Let a = {a, b, c} and R = {(a, a), (b, b), (c, c), (b, c), (a, b)} be a relation on A, then the