# If x/y=(a+2)/(a-2), then the value of (x²-y²)/( x²+y²) is

- 4a/(a
^{2}+4) - 2a/ (a
^{2}+4) - 4a/(a
^{2}+2) - 2a/ (a
^{2}+2)

**Answer: (1) 4a/(a² + 4)**

**Explanation:-
**x/y = (a + 2)/(a – 2)

Then, x = a + 2 & y = a – 2

x² = (a + 2)² & y² = (a – 2)²

x² = a² + 2² + 2 x a x 2 & y² = a² + 2² – 2 x a x 2

x² = a² + 4 + 4 a & y² = a² + 4 – 4a

Then, x² – y² = a² + 4 + 4 a – a² – 4 + 4 a

x² – y² = 4 a + 4 a = 8 a ………………………… (1)

And x² + y² = a² + 4 + 4 a + a² + 4 – 4a

= 2 a² + 8

x² + y² = 2 (a² +4) ……………………….. (2)

Then, (x² – y²)/(x² + y²) = 8 a/2 (a² +4) {(From equation (1) & (2)}

= 4 a/(a² +4)

Hence, the answer is (1) 4 a/(a² +4).