Ln(x+5)=-ln(x-1)-ln(x+1)

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Solution for Ln(x+5)=-ln(x-1)-ln(x+1) equation: 


Simplifying
Ln(x + 5) = -1ln(x + -1) + -1ln(x + 1)

Reorder the terms:
nL(5 + x) = -1ln(x + -1) + -1ln(x + 1)
(5 * nL + x * nL) = -1ln(x + -1) + -1ln(x + 1)
(5nL + nxL) = -1ln(x + -1) + -1ln(x + 1)

Reorder the terms:
5nL + nxL = -1ln(-1 + x) + -1ln(x + 1)
5nL + nxL = (-1 * -1ln + x * -1ln) + -1ln(x + 1)
5nL + nxL = (1ln + -1lnx) + -1ln(x + 1)

Reorder the terms:
5nL + nxL = 1ln + -1lnx + -1ln(1 + x)
5nL + nxL = 1ln + -1lnx + (1 * -1ln + x * -1ln)
5nL + nxL = 1ln + -1lnx + (-1ln + -1lnx)

Reorder the terms:
5nL + nxL = 1ln + -1ln + -1lnx + -1lnx

Combine like terms: 1ln + -1ln = 0
5nL + nxL = 0 + -1lnx + -1lnx
5nL + nxL = -1lnx + -1lnx

Combine like terms: -1lnx + -1lnx = -2lnx
5nL + nxL = -2lnx

Solving
5nL + nxL = -2lnx

Solving for variable 'n'.

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

Add '2lnx' to each side of the equation.
5nL + 2lnx + nxL = -2lnx + 2lnx

Reorder the terms:
2lnx + 5nL + nxL = -2lnx + 2lnx

Combine like terms: -2lnx + 2lnx = 0
2lnx + 5nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(2lx + 5L + xL) = 0


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

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(2lx + 5L + xL)' equal to zero and attempt to solve:

Simplifying
2lx + 5L + xL = 0

Reorder the terms:
5L + 2lx + xL = 0

Solving
5L + 2lx + xL = 0

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

Add '-5L' to each side of the equation.
5L + 2lx + -5L + xL = 0 + -5L

Reorder the terms:
5L + -5L + 2lx + xL = 0 + -5L

Combine like terms: 5L + -5L = 0
0 + 2lx + xL = 0 + -5L
2lx + xL = 0 + -5L
Remove the zero:
2lx + xL = -5L

Add '-2lx' to each side of the equation.
2lx + -2lx + xL = -5L + -2lx

Combine like terms: 2lx + -2lx = 0
0 + xL = -5L + -2lx
xL = -5L + -2lx

Add '-1xL' to each side of the equation.
xL + -1xL = -5L + -2lx + -1xL

Combine like terms: xL + -1xL = 0
0 = -5L + -2lx + -1xL

Simplifying
0 = -5L + -2lx + -1xL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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