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Category - Math

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If x⊞y = (x + y)/(x − y), x⊟y = (x − y)/(x + y), x^* = 2x/(x − y) and y^* = 2y/(x + y), what is the value of (x⊞y) − (x⊟y)?
  1. 2y
  2. 2x − 2y
  3. x^* + y^*
  4. x^* − y^*
  5. x^* y^*
Explanation
Answer: E - The value of (x⊞y) − (x⊟y) is x^* y^*. Simplify the expression
(x⊞y) − (x⊟y) = (x + y)/(x − y) − (x − y)/(x + y) = ((x + y)2 − (x − y)2)/(x − y)(x + y) =
= (x2 + 2xy + y2 − (x2 − 2xy + y2 ))/(x − y)(x + y) = (x2 + 2xy + y2 − x2 + 2xy − y2)/(x − y)(x + y) = 4xy/(x − y)(x + y) =
= 2x/((x − y) ) 2y/((x + y) ) = x^* y^*
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