Ln(x+1)-ln(x-1)2=0

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Solution for Ln(x+1)-ln(x-1)2=0 equation:


Simplifying
Ln(x + 1) + -1ln(x + -1) * 2 = 0

Reorder the terms:
nL(1 + x) + -1ln(x + -1) * 2 = 0
(1 * nL + x * nL) + -1ln(x + -1) * 2 = 0
(1nL + nxL) + -1ln(x + -1) * 2 = 0

Reorder the terms:
1nL + nxL + -1ln(-1 + x) * 2 = 0

Reorder the terms for easier multiplication:
1nL + nxL + -1 * 2ln(-1 + x) = 0

Multiply -1 * 2
1nL + nxL + -2ln(-1 + x) = 0
1nL + nxL + (-1 * -2ln + x * -2ln) = 0
1nL + nxL + (2ln + -2lnx) = 0

Reorder the terms:
2ln + -2lnx + 1nL + nxL = 0

Solving
2ln + -2lnx + 1nL + nxL = 0

Solving for variable 'l'.

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

Add '-1nL' to each side of the equation.
2ln + -2lnx + 1nL + -1nL + nxL = 0 + -1nL

Combine like terms: 1nL + -1nL = 0
2ln + -2lnx + 0 + nxL = 0 + -1nL
2ln + -2lnx + nxL = 0 + -1nL
Remove the zero:
2ln + -2lnx + nxL = -1nL

Add '-1nxL' to each side of the equation.
2ln + -2lnx + nxL + -1nxL = -1nL + -1nxL

Combine like terms: nxL + -1nxL = 0
2ln + -2lnx + 0 = -1nL + -1nxL
2ln + -2lnx = -1nL + -1nxL

Reorder the terms:
2ln + -2lnx + nL + nxL = -1nL + nL + -1nxL + nxL

Combine like terms: -1nL + nL = 0
2ln + -2lnx + nL + nxL = 0 + -1nxL + nxL
2ln + -2lnx + nL + nxL = -1nxL + nxL

Combine like terms: -1nxL + nxL = 0
2ln + -2lnx + nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(2l + -2lx + L + 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 l to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n 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 '(2l + -2lx + L + xL)' equal to zero and attempt to solve: Simplifying 2l + -2lx + L + xL = 0 Reorder the terms: L + 2l + -2lx + xL = 0 Solving L + 2l + -2lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-1L' to each side of the equation. L + 2l + -2lx + -1L + xL = 0 + -1L Reorder the terms: L + -1L + 2l + -2lx + xL = 0 + -1L Combine like terms: L + -1L = 0 0 + 2l + -2lx + xL = 0 + -1L 2l + -2lx + xL = 0 + -1L Remove the zero: 2l + -2lx + xL = -1L Add '-1xL' to each side of the equation. 2l + -2lx + xL + -1xL = -1L + -1xL Combine like terms: xL + -1xL = 0 2l + -2lx + 0 = -1L + -1xL 2l + -2lx = -1L + -1xL 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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