If x + y - 4t = 0 then find the value of ^@ \dfrac{ x } { x - 2t } + \dfrac{ 2t } { y - 2t} ^@.


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Answer:

1

Step by Step Explanation:
  1. We are given x + y - 4t = 0
    It can also be written as: (x - 2t) + (y - 2t) = 0
    or (x - 2t) = -(y - 2t)
  2. The above step tells us that we may replace (x - 2t) with -(y - 2t) wherever needed.
  3. We need to find the value of ^@ \dfrac{ x } { x - 2t } + \dfrac{ 2t } { y - 2t} ^@ which is equal to:
     
    x
    -(y - 2t)
      +  
    2t
    y - 2t
     
    =  
    -x + 2t
    y - 2t
     
    =  
    -(x - 2t)
    (y - 2t)
     
  4. As we know that (x - 2t) = -(y - 2t), the answer to the above question becomes 1.

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