Question

If a = 4xy/x+y, find the value of a+2x/a-2x+a+2y/a-2y in most simplified form?

Answer 1

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.

Answer 2

Answer:

Step-by-step explanation: