\text{x}\over \text{y} = \text{a + 2}\over \text{a - 2}

squaring both side

or, \text{x²}\over \text{y²}= \text{(a + 2)²}\over \text{(a - 2)²}

Applying componendo and dividendo

\text{x² + y²}\over \text{x² - y²} = \text{(a + 2)² + (a - 2)²}\over \text{(a + 2)² + (a - 2)²}

= \text{(a + 2)² + (a - 2)²}\over \text{(a + 2)² - (a - 2)²}

= \text{2(a² + 4)}\over \text{8a}

= \text{a² + 4}\over \text{4a}

∴ \text{x² - y²}\over \text{x² + y²} = \text{4a}\over \text{a² + 4}