$$\frac{\left(a+\frac{1}{b}\right)^{x}\left(a-\frac{1}{b}\right)^{y}}{\left(b +\frac{1}{a}\right)^{x}\left(b -\frac{1}{a}\right)^{y}}$$=

A

$$\left(\frac{a}{b}\right)^{x-y}$$

B

$$\left(\frac{a}{b}\right)^{x+y}$$

C

$$a^{x}.b$$

D

$$a^{y}.b^{x}$$