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? Options: A . &nbsp$$\frac{{{a^2} - {b^2}}}{{ab}}$$ B . &nbsp$$\frac{{{a^2} + {b^2}}}{{2ab}}$$ C . &nbsp$$\frac{{{a^2} - {b^2}}}{{2ab}}$$ D . &nbsp$$\frac{{2ab}}{{{a^2} - {b^2}}}$$

If $$\frac{{x + 1}}{{x - 1}} = \frac{a}{b}$$ and $$\frac{{1

Question

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?

Options:

A . $$\frac{{{a^2} - {b^2}}}{{ab}}$$

B . $$\frac{{{a^2} + {b^2}}}{{2ab}}$$

C . $$\frac{{{a^2} - {b^2}}}{{2ab}}$$

D . $$\frac{{2ab}}{{{a^2} - {b^2}}}$$

Answer: Option D

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