If `(x^(3) + 3xy^(2))/(3x^(2)y + y^(3)) = (m^(3) + 3mn^(2))/(3m^(2)n + n^(3))`, show that : `nx = my`.

If (m + n)/(m + 3n) = (2)/(3) , find : (2n^(2))/(3m^(2) + mn) .

Add : x^(3) - x^(2)y + 5xy^(2) + y^(3) , -x^(3) - 9xy^(2) + y^(3), 3x^(2)y + 9xy^(2)

The two curves x^(3) - 3xy^(2) + 2 = 0 and 3x^(2) y - y^(3) = 2

Simplify: 2x^(2)+3xy -3y^(2)+x^(2)-xy+y^(2)

If x+y+z=xyz , prove that: a) (3x-x^(3))/(1-3x^(2))+(3y-y^(3))/(1-3y^(2))+(3z-z^(3))/(1-3z^(2))= (3x-x^(3))/(1-3x^(2)).(3y-y^(3))/(1-3y^(2)).(3z-z^(3))/(1-3z^(2)) b) (x+y)/(1-xy) + (y+z)/(1-yz)+(z+x)/(1-zx)= (x+y)/(1-xy) .(y+z)/(1-yz).(z+x)/(1-zx)

Simplify: (16 m^3y^2)/(4m^2y) (2) (32 m^2n^3p^2)/(4m n p)

If y=1+x+(x^(2))/(2!)+(x^(3))/(3!)+....+(x^(n))/(n!) , then show that (dy)/(dx)+(x^(n))/(n!)=y

{:(2x + y = (7xy)/(3)),(x + 3y = (11xy)/(3)):}