(x+y)(1+xy)=(x*x+1)(y*y+1)

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Solution for (x+y)(1+xy)=(x*x+1)(y*y+1) equation: 


Simplifying
(x + y)(1 + xy) = (x * x + 1)(y * y + 1)

Multiply (x + y) * (1 + xy)
(x(1 + xy) + y(1 + xy)) = (x * x + 1)(y * y + 1)
((1 * x + xy * x) + y(1 + xy)) = (x * x + 1)(y * y + 1)
((1x + x2y) + y(1 + xy)) = (x * x + 1)(y * y + 1)
(1x + x2y + (1 * y + xy * y)) = (x * x + 1)(y * y + 1)

Reorder the terms:
(1x + x2y + (xy2 + 1y)) = (x * x + 1)(y * y + 1)
(1x + x2y + (xy2 + 1y)) = (x * x + 1)(y * y + 1)

Reorder the terms:
(1x + xy2 + x2y + 1y) = (x * x + 1)(y * y + 1)
(1x + xy2 + x2y + 1y) = (x * x + 1)(y * y + 1)

Multiply x * x
1x + xy2 + x2y + 1y = (x2 + 1)(y * y + 1)

Reorder the terms:
1x + xy2 + x2y + 1y = (1 + x2)(y * y + 1)

Multiply y * y
1x + xy2 + x2y + 1y = (1 + x2)(y2 + 1)

Reorder the terms:
1x + xy2 + x2y + 1y = (1 + x2)(1 + y2)

Multiply (1 + x2) * (1 + y2)
1x + xy2 + x2y + 1y = (1(1 + y2) + x2(1 + y2))
1x + xy2 + x2y + 1y = ((1 * 1 + y2 * 1) + x2(1 + y2))
1x + xy2 + x2y + 1y = ((1 + 1y2) + x2(1 + y2))
1x + xy2 + x2y + 1y = (1 + 1y2 + (1 * x2 + y2 * x2))
1x + xy2 + x2y + 1y = (1 + 1y2 + (1x2 + x2y2))

Reorder the terms:
1x + xy2 + x2y + 1y = (1 + 1x2 + x2y2 + 1y2)
1x + xy2 + x2y + 1y = (1 + 1x2 + x2y2 + 1y2)

Solving
1x + xy2 + x2y + 1y = 1 + 1x2 + x2y2 + 1y2

Solving for variable 'x'.

Reorder the terms:
-1 + 1x + xy2 + -1x2 + x2y + -1x2y2 + 1y + -1y2 = 1 + 1x2 + x2y2 + 1y2 + -1 + -1x2 + -1x2y2 + -1y2

Reorder the terms:
-1 + 1x + xy2 + -1x2 + x2y + -1x2y2 + 1y + -1y2 = 1 + -1 + 1x2 + -1x2 + x2y2 + -1x2y2 + 1y2 + -1y2

Combine like terms: 1 + -1 = 0
-1 + 1x + xy2 + -1x2 + x2y + -1x2y2 + 1y + -1y2 = 0 + 1x2 + -1x2 + x2y2 + -1x2y2 + 1y2 + -1y2
-1 + 1x + xy2 + -1x2 + x2y + -1x2y2 + 1y + -1y2 = 1x2 + -1x2 + x2y2 + -1x2y2 + 1y2 + -1y2

Combine like terms: 1x2 + -1x2 = 0
-1 + 1x + xy2 + -1x2 + x2y + -1x2y2 + 1y + -1y2 = 0 + x2y2 + -1x2y2 + 1y2 + -1y2
-1 + 1x + xy2 + -1x2 + x2y + -1x2y2 + 1y + -1y2 = x2y2 + -1x2y2 + 1y2 + -1y2

Combine like terms: x2y2 + -1x2y2 = 0
-1 + 1x + xy2 + -1x2 + x2y + -1x2y2 + 1y + -1y2 = 0 + 1y2 + -1y2
-1 + 1x + xy2 + -1x2 + x2y + -1x2y2 + 1y + -1y2 = 1y2 + -1y2

Combine like terms: 1y2 + -1y2 = 0
-1 + 1x + xy2 + -1x2 + x2y + -1x2y2 + 1y + -1y2 = 0

The solution to this equation could not be determined.

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