QQuestion
If x\over y = (a + 2)\over (a - 2), then find the value of (x² - y²)\over (x² + y²)
✓Answer
\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}
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