f(x)f(y)-xy=f(x)+f(y)-1

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


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

Multiply f * x
fx * f * y + -1xy = f(x) + f(y) + -1

Multiply fx * f
f2x * y + -1xy = f(x) + f(y) + -1

Multiply f2x * y
f2xy + -1xy = f(x) + f(y) + -1

Multiply f * x
f2xy + -1xy = fx + f(y) + -1

Multiply f * y
f2xy + -1xy = fx + fy + -1

Reorder the terms:
f2xy + -1xy = -1 + fx + fy

Solving
f2xy + -1xy = -1 + fx + fy

Solving for variable 'f'.

Reorder the terms:
1 + -1fx + -1fy + f2xy + -1xy = -1 + fx + fy + 1 + -1fx + -1fy

Reorder the terms:
1 + -1fx + -1fy + f2xy + -1xy = -1 + 1 + fx + -1fx + fy + -1fy

Combine like terms: -1 + 1 = 0
1 + -1fx + -1fy + f2xy + -1xy = 0 + fx + -1fx + fy + -1fy
1 + -1fx + -1fy + f2xy + -1xy = fx + -1fx + fy + -1fy

Combine like terms: fx + -1fx = 0
1 + -1fx + -1fy + f2xy + -1xy = 0 + fy + -1fy
1 + -1fx + -1fy + f2xy + -1xy = fy + -1fy

Combine like terms: fy + -1fy = 0
1 + -1fx + -1fy + f2xy + -1xy = 0

The solution to this equation could not be determined.

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