Chapter 10 - Radical Expressions and Equations - 10-3 Operations with Radial Expressions - Practice and Problem-Solving Exercises - Page 616: 35

$\frac{7\sqrt{13}-7\sqrt{5}}{8}$

Multiply using the conjugate. Remember that $(a^2-b^2)=(a+b)(a-b)$. $\frac{7}{\sqrt{5}+\sqrt{13}}\cdot \frac{\sqrt{5}-\sqrt{13}}{\sqrt{5}-\sqrt{13}}=\frac{7\sqrt{5}-7\sqrt{13}}{5-13}=\frac{7\sqrt{5}-7\sqrt{13}}{-8}=\frac{7\sqrt{13}-7\sqrt{5}}{8}$