Question 33539
first  simplify the numerator and denominator seperately .

 1) denominator- on simplifying,
      6/x - 8/y
 
    we get,
      (6y -8x)/xy  ---------   A

 2) Numerator -

      (36y^2 -64x^2)  / xy
 try to simplify this,
   
     ( 36y^2- 64x^2) can be written as

 6^2 y^2 - 8^2 x^2     there is a formula( a^2-b^2 = (a+b)(a-b)therefore here a=6y and b= 8x)

from that the above can be re-written as (6y-8x)(6y +8x)

now the new NUMERATOR IS 
                (6y-8x)(6y+8x)/xy  -------------- B

  FROM A & B,

        (6y-8x)(6y+8x)  * xy                    
    ___________________________              
           xy       * (6y-8x)                  


    =     (6y+8x)  is the answer.   (xy  and (6y-8x)get cancelled  )

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priya