if a = 4xy/x+y , the value of a+2x/a-2x+ a+2y/a-2y in most simplified form ??
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Given, a = 4xy/x+y ...(i)
Now, a+2x/a-2x + a+2y/a-2y
= 4xy/x+y+2x/4xy/x+y-2x + 4xy/x+y+2y/4xy/x+y-2y [From Eq. 1]
= 4xy+2x(x+y)/(x+y)/4xy-2x(x+y)/(x+y) + 4xy+2y(x+y)/(x+y)/4xy-2y(x+y)/(x+y)
= 4xy+2x²+2xy/ 4xy-2x²-2xy + 4xy+2xy+2y²/4xy-2xy-2y²
= 6xy+2x²/2xy-2x² + 6xy+2y²/2xy-2y²
= 2x(3y+x)/2x(y-x)+2y(3x+y)/2y(x-y)
= 3y+x/y-x - 3x+y/y-x
= 3y+x-3x-y/(y-x)
= 2y-2x/(y-x)
= 2(y-x)/(y-x)
= 2 ans.
Now, a+2x/a-2x + a+2y/a-2y
= 4xy/x+y+2x/4xy/x+y-2x + 4xy/x+y+2y/4xy/x+y-2y [From Eq. 1]
= 4xy+2x(x+y)/(x+y)/4xy-2x(x+y)/(x+y) + 4xy+2y(x+y)/(x+y)/4xy-2y(x+y)/(x+y)
= 4xy+2x²+2xy/ 4xy-2x²-2xy + 4xy+2xy+2y²/4xy-2xy-2y²
= 6xy+2x²/2xy-2x² + 6xy+2y²/2xy-2y²
= 2x(3y+x)/2x(y-x)+2y(3x+y)/2y(x-y)
= 3y+x/y-x - 3x+y/y-x
= 3y+x-3x-y/(y-x)
= 2y-2x/(y-x)
= 2(y-x)/(y-x)
= 2 ans.
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