I need help with this problem:
Let a and b be rational integers. If $\frac{(\sqrt3+\sqrt2)^3}{(\sqrt3-\sqrt2)} = a + b\sqrt6$, find a and b.
I don't know exactly how to approach the problem. I know there must be some condition that will allow only specific values to be possible, but I don't know what that is, besides the fact that it must have something to do with being able to express the numbers as fractions.
Hint: Note that $$\frac{(\sqrt3+\sqrt2)^3}{(\sqrt3-\sqrt2)} = \frac{(\sqrt3+\sqrt2)^4}{(\sqrt3-\sqrt2)(\sqrt3+\sqrt2)}=(\sqrt3+\sqrt2)^4$$
You can then expand the expression and compare the coefficients.