Find a common denominator for the two fractions.

The denominators are conjugates: $(2\sqrt{7} - 3\sqrt{3})$ and $(2\sqrt{7} + 3\sqrt{3})$. Their product is of the form $(a-b)(a+b) = a^2 - b^2$.

$$(2\sqrt{7} - 3\sqrt{3})(2\sqrt{7} + 3\sqrt{3}) = (2\sqrt{7})^2 - (3\sqrt{3})^2$$ $$= (4 \times 7) - (9 \times 3)$$ $$= 28 - 27$$ $$= 1$$