Answer
$\frac{13 + \sqrt 65 + \sqrt 130 + 5 \sqrt 2}{8} $
Work Step by Step
$\frac{\sqrt 13 + \sqrt 10}{\sqrt 13 - \sqrt 5} \times \frac{\sqrt 13 + \sqrt 5}{\sqrt 13 + \sqrt 5}$
Use FOIL to simplify. FOIL: First (Multiply the first variables in the brackets), outside (Multiply the outer variables), Inside (Multiply the inside variables), Last (Multiply the last variables in the brackets).
$\frac{13 + \sqrt 13 \sqrt 5 + \sqrt 10 \sqrt 13 + \sqrt 10 \sqrt 5}{13 - 5} $
We multiply the radicals and bring them under the same radical
$\frac{13 + (\sqrt 13 \times 5) + (\sqrt 10 \times 13) + (\sqrt 10 \times 5)}{13 - 5} $
$\frac{13 + (\sqrt 65) + (\sqrt 130) + (5 \sqrt 2)}{8} $
We can no longer simplify the radicals and the denominator so the answer is
$\frac{13 + \sqrt 65 + \sqrt 130 + 5 \sqrt 2}{8} $
