# How do you rationalize and divide (2+sqrt3) /(2-sqrt3)?

Using the identity $\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$, let's multiply and divide the fraction by $2 + \setminus \sqrt{3}$. You'll notice that, when doing so, at the numerator you'll have ${\left(2 + \setminus \sqrt{3}\right)}^{2}$, while at the denominator you'll have $\left(2 - \setminus \sqrt{3}\right) \left(2 + \setminus \sqrt{3}\right)$, which is the formula mentioned at the beginning.
So, $\left(2 - \setminus \sqrt{3}\right) \left(2 + \setminus \sqrt{3}\right) = {2}^{2} - {\left(\setminus \sqrt{3}\right)}^{2} = 4 - 3 = 1$.
Since the denominator is $1$, we can ignore it, and the final answer is thus ${\left(2 + \setminus \sqrt{3}\right)}^{2}$