If `(2x-3y)/(3z+y)=(z-y)/(z-x)=(x+3z)/(2y-3x)`, then prove that every ratio is `x/y`

If (3x-5y)/5z+3y)=(x+5z)/(y-5x)=(y-z)/(x-z) then show that each ratio is x/y .

If (x)/(y+z-x)=(y)/(z+x-y)=(z)/(x+y-z) and x+y+z=0 then show that each ratio is equal to .

If (ax+by)/(x+y)=(bx+az)/(x+z)=(ay+bz)/(y+z) and x+y+z=!0 then show that each ratio is (a+b)/2

If x/(3x-y-z)=(y)/(3y-z-x)=(z)/(3z-x-y) and x+y+z=0 then show that the value of each of the ratio is equal to 1.

If x/(x+2y+z) = y/(y+2z+x) = z/(z+2x +y) and x+y+z !=0 , then show that each ratio is equal to 1/4 .

If x/(3x-y-z) =y/(3y-z-x) =z/(3z-x-y) and x+y+z != 0 , then show that the value of each raio is equal to 1.

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

If [(1,2,3),(2,4,1),(3,2,9)][(x),(y),(z)]=[(6),(7),(14)] , then the values of x, y, z respectively are