if `|[a,y,z],[x,b,z],[x,y,c]|=0`, then prove that `a/(a-x) + b/(b-y) + c/(c-z)=2`

If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b ,c-z],[ a-x, b-y, c]|=0, then the value of the expression a/x+b/y+c/z is a. 0 b. -1 c. 1 d. 2

If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b ,c-z],[ a-x, b-y, c]|=0, then the value of the expression a/x+b/y+c/z is a. 0 b. -1 c. 1 d. 2

If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b ,c-z],[ a-x, b-y, c]|=0, then the value of the expression a/x+b/y+c/z is 0 b. -1 c. 1 d. 2

If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b ,c-z],[ a-x, b-y, c]|=0, then the value of the expression a/x+b/y+c/z is 0 b. -1 c. 1 d. 2

If x=b-c+a, y=c-a+b, z=a-b+c , then prove that (b-a) x + (c-b)y +(a-c)z=0

If x/(b +c) = y/(c+a) = z/(a + b) , then show that a/(y+z-x) = b/(z+x - y) = c/(x + y - z) .

If b+c-a/x+y-x = c+a-b/c+x-y = a+b_c/x+y-z, then prove that a/x = b/y = c/z.

If a/(y+z) = b/(z + x) = c/(x+y) , then prove that (a(b-c))/(y^(2)-z^(2)) = (b(c-a))/(z^(2)-x^(2)) = (c(a-b))/(x^(2)-y^(2)) .

If (y/z)^a (z/x)^b (x/y)^c=1 , then prove that (y/z)^((1)/(b-c))=(z/x)^((1)/(c-a))=(x/y)^((1)/(a-b)) .