Question

For all x > 0 and y > 0, the radical expression
(√x)÷(3√x-√y)s equivalent to:

Answer 1

`(√(x))/(3√(x)-√(y))=(√(x))/(3√(x)-√(y))\cdot(3√(x)+√(y))/(3√(x)+√(y))=(3(√(x))^2+(√(x))(√(y)))/((3√(x))^2-(√(y))^2)\\\\=(3x+√(xy))/(9x-y)\\\\Used:\\(a-b)(a+b)=a^2-b^2\\\\(√(a))^2=a\ for\ a\geq0\\\\√(a)\cdot√(b)=√(ab)\ for\ a,b\geq0`