Answer
$\displaystyle \frac{77+11\sqrt{3}}{46}$
Work Step by Step
Rationalize the denominator using the difference of squares,
$(a+b)(a-b)=a^{2}-b^{2}$
$\displaystyle \frac{11}{7-\sqrt{3}}\cdot\frac{7+\sqrt{3}}{7+\sqrt{3}}=\frac{11(7+\sqrt{3})}{7^{2}-(\sqrt{3})^{2}}$
$=\displaystyle \frac{77+11\sqrt{3}}{49-3}$
= $\displaystyle \frac{77+11\sqrt{3}}{46}$
