= = Taking the first two fractions = Cross multiplying: {x(c+a-b) = y(b+c-a) x(-b+c+a) = y[b+(c-a)] x[(-b+c)+a] = yb+y(c-a) x[-(b-c)+a] = yb+y(c-a) -x(b-c)+xa = yb+y(c-a) xa-yb = x(b-c)+y(c-a) <--- equation (1) Taking the first and third fractions: = x(a+b-c) = z(b+c-a) x[a+(b-c)] = z(-a+b+c) xa+x(b-c) = z[(-a+b)+c] xa+x(b-c) = z[-(a-b)+c] xa+x(b-c) = -z(a-b)+zc x(b-c)+z(a-b) = zc-xa <--- equation (2) Taking the second and third fractions: = Cross-multiplying: y(a+b-c) = z(c+a-b) y(-c+a+b) = z[c+(a-b)] y[(-c+a)+b] = zc+z(a-b) y[-(c-a)+b] = zc+z(a-b) -y(c-a)+yb = zc+z(a-b) yb-zc = y(c-a)+z(a-b) <--- equation (3) Putting equations (1), (2), and (3) together xa-yb = x(b-c)+y(c-a) <--- equation (1) x(b-c)+z(a+b) = zc-xa <--- equation (2) yb-zc = y(c-a)+z(a-b) <--- equation (3) Reversing equation (2) xa-yb = x(b-c)+y(c-a) <--- equation (1) xc-xa = x(b-c)+z(a-b) <--- equation (2) yb-zc = y(c-a)+z(a-b) <--- equation (3) Adding all three equation (equals added to equals give equals) xc-zc =2x(b-c)+2y(c-a)+2z(a-b) Dividing through by 2 = x(b-c)+y(c-a)+z(a-b) or if you like: (b-c)x+(c-a)y+(a-b)z = Edwin
