If $$\frac{{x + 1}}{{x - 1}} = \frac{a}{b}$$and $$\frac{{1 - y}}{{1 + y}} = \frac{b}{a}{\text{,}}$$then the value of $$\frac{{x - y}}{{1 + xy}}$$is?

• A. $\frac{{{a^2} - {b^2}}}{{ab}}$$
• B. $\frac{{{a^2} + {b^2}}}{{2ab}}$$
• C. $\frac{{{a^2} - {b^2}}}{{2ab}}$$
• D. $\frac{{2ab}}{{{a^2} - {b^2}}}$$