xf(y)+yf(x)=(x+y)f(x)f(y)

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Solution for xf(y)+yf(x)=(x+y)f(x)f(y) equation: 


Simplifying
xf(y) + yf(x) = (x + y) * f(x) * f(y)

Multiply fx * y
fxy + yf(x) = (x + y) * f(x) * f(y)

Multiply fy * x
fxy + fxy = (x + y) * f(x) * f(y)

Combine like terms: fxy + fxy = 2fxy
2fxy = (x + y) * f(x) * f(y)

Reorder the terms for easier multiplication:
2fxy = f * x * f * y(x + y)

Multiply f * x
2fxy = fx * f * y(x + y)

Multiply fx * f
2fxy = f2x * y(x + y)

Multiply f2x * y
2fxy = f2xy(x + y)
2fxy = (x * f2xy + y * f2xy)

Reorder the terms:
2fxy = (f2xy2 + f2x2y)
2fxy = (f2xy2 + f2x2y)

Solving
2fxy = f2xy2 + f2x2y

Solving for variable 'f'.

Reorder the terms:
2fxy + -1f2xy2 + -1f2x2y = f2xy2 + -1f2xy2 + f2x2y + -1f2x2y

Combine like terms: f2xy2 + -1f2xy2 = 0
2fxy + -1f2xy2 + -1f2x2y = 0 + f2x2y + -1f2x2y
2fxy + -1f2xy2 + -1f2x2y = f2x2y + -1f2x2y

Combine like terms: f2x2y + -1f2x2y = 0
2fxy + -1f2xy2 + -1f2x2y = 0

Factor out the Greatest Common Factor (GCF), 'fxy'.
fxy(2 + -1fy + -1fx) = 0


Subproblem 1
Set the factor 'fxy' equal to zero and attempt to solve:

Simplifying
fxy = 0

Solving
fxy = 0

Move all terms containing f to the left, all other terms to the right.

Simplifying
fxy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(2 + -1fy + -1fx)' equal to zero and attempt to solve:

Simplifying
2 + -1fy + -1fx = 0

Reorder the terms:
2 + -1fx + -1fy = 0

Solving
2 + -1fx + -1fy = 0

Move all terms containing f to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -1fx + -2 + -1fy = 0 + -2

Reorder the terms:
2 + -2 + -1fx + -1fy = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1fx + -1fy = 0 + -2
-1fx + -1fy = 0 + -2

Combine like terms: 0 + -2 = -2
-1fx + -1fy = -2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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