A Nested Fraction at Two

At $x=2$ $$\frac{x+\frac{1}{x+\frac{1}{x+\frac{1}{x}}}}{x-\frac{1}{x-\frac{1}{x-\frac{1}{x}}}} = \frac{a}{b}$$If $a$ and $b$ are coprime positive integers, what is the value of $a+b$?