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

  1. 4a/(a2+4)
  2. 2a/ (a2+4)
  3. 4a/(a2+2)
  4. 2a/ (a2+2)
Monis Rasool Professor Asked on 21st November 2015 in Maths.
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2 Answer(s)

Answer: (1) 4a/(a² + 4)

 

sujeetstar24 Newbie Answered on 21st November 2015.
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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).

Anurag Mishra Professor Answered on 23rd November 2015.
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