Answer
The answer is as follows: $(7\sqrt13-7\sqrt5)\div8$.
Work Step by Step
We can solve the expression as follows:
$= 7\div(\sqrt5+\sqrt13)$
$= 7\div(\sqrt5+\sqrt13)*(\sqrt5-\sqrt13)/(\sqrt5-\sqrt13)$
(Multiply and divide by $(\sqrt5-\sqrt13)$)
$= 7*(\sqrt5-\sqrt13)/(\sqrt5^{2}-\sqrt13^{2})$
(since $(a+b)(a-b)=a^{2}-b^{2}$)
$= (7\sqrt5-7\sqrt13)\div(5-13)$
$= (7\sqrt5-7\sqrt13)\div(-8)$
$= (7\sqrt13-7\sqrt5)\div8$
(Multiply and divide by -1.)
