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

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

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

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

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

Remove parenthesis around (-1 + x)
5ln + lnx = -1 + x + -1ln(x + 1)

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

Reorder the terms:
5ln + lnx = -1 + -1ln + -1lnx + x

Solving
5ln + lnx = -1 + -1ln + -1lnx + x

Solving for variable 'l'.

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

Add 'ln' to each side of the equation.
5ln + ln + lnx = -1 + -1ln + -1lnx + ln + x

Combine like terms: 5ln + ln = 6ln
6ln + lnx = -1 + -1ln + -1lnx + ln + x

Reorder the terms:
6ln + lnx = -1 + -1ln + ln + -1lnx + x

Combine like terms: -1ln + ln = 0
6ln + lnx = -1 + 0 + -1lnx + x
6ln + lnx = -1 + -1lnx + x

Add 'lnx' to each side of the equation.
6ln + lnx + lnx = -1 + -1lnx + lnx + x

Combine like terms: lnx + lnx = 2lnx
6ln + 2lnx = -1 + -1lnx + lnx + x

Combine like terms: -1lnx + lnx = 0
6ln + 2lnx = -1 + 0 + x
6ln + 2lnx = -1 + x

Reorder the terms:
1 + 6ln + 2lnx + -1x = -1 + x + 1 + -1x

Reorder the terms:
1 + 6ln + 2lnx + -1x = -1 + 1 + x + -1x

Combine like terms: -1 + 1 = 0
1 + 6ln + 2lnx + -1x = 0 + x + -1x
1 + 6ln + 2lnx + -1x = x + -1x

Combine like terms: x + -1x = 0
1 + 6ln + 2lnx + -1x = 0

The solution to this equation could not be determined.