Rationalizing denominator of $\frac{7}{2+\sqrt{3}}$. Cannot match textbook solution

Question

I am given this expression and asked to simplify by rationalizing the denominator:

$$\frac{7}{2+\sqrt{3}}$$

The solution is provided:

$14 – 7\sqrt{3}$

I was able to get to this in the numerator but am left with a 4 in the denominator. Here are my steps:

$$\frac{7}{2+\sqrt{3}} * \frac{2-\sqrt{3}}{2-\sqrt{3}}$$

=

$$\frac{14 – 7\sqrt{3}}{4}$$

Presumably I should not have a denominator here since the solution I'm given is just whats in the numerator. Presumably my numerator calculation is correct, where did I go wrong on the denominator?

Answer 1

Note that $\left(2+\sqrt3\right)\times\left(2-\sqrt3\right)=4-3=1$.