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

If a(y+z)=b(z+x)=c(x+y) then show that (a-b)/(x^(2)-y^(2))=(b-c)/(y^(2)-z^(2))=(c-a)/(z^(2)-x^(2))]

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

a(y+z)=x,b(z+x)=y,c(x+y)=z prove that (x^(2))/(a(1-bc))=(y^(2))/(b(1-ca))=(z^(2))/(c(1-ab))

If a^(x)=b^(y)=c^(z) and b^(2)=ac, then show that y=(2zx)/(z+x)

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)/(a)=(y)/(b)=(z)/(c), then show that (x^(3)+a^(3))/(x^(2)+a^(2))+(y^(3)+b^(3))/(y^(2)+b^(2))+(z^(3)+c^(3))/(z^(2)+c^(2))=((x+y+z)^(3)+(a+b+c)^(2))/((x+b+z)^(2)+(a+b+c)^(2))

If (a+b)/(x)=(b+c)/(y)=(c+a)/(z), then (A) (a+b+c)/(x+y+z)=(ab+bc+ca)/(ay+bz+cx)(B)(c)/(y+z-x)=(a)/(x+z-y)=(b)/(x+y-z)(C)(c)/(x)=(a)/(y)=(b)/(z)(D)(a+b)/(b+c)=(a+b+x)/(b+c+y)

If (2y + 2z - x)/a = (2z + 2x - y)/b = (2x + 2y - z)/c ,then show that (9x)/(2b + 2c - a) = (9y)/(2c + 2a - b) = (9z)/(2a + 2b - c)

a^(x)=b^(y)=c^(z) and b^(2)=ac then prove that (1)/(x)+(1)/(z)=(2)/(y)