In(x+3)-In(x-1)=In(x+2)-In(x+3)

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Solution for In(x+3)-In(x-1)=In(x+2)-In(x+3) equation: 


Simplifying
In(x + 3) + -1In(x + -1) = In(x + 2) + -1In(x + 3)

Reorder the terms:
nI(3 + x) + -1In(x + -1) = In(x + 2) + -1In(x + 3)
(3 * nI + x * nI) + -1In(x + -1) = In(x + 2) + -1In(x + 3)
(3nI + nxI) + -1In(x + -1) = In(x + 2) + -1In(x + 3)

Reorder the terms:
3nI + nxI + -1nI(-1 + x) = In(x + 2) + -1In(x + 3)
3nI + nxI + (-1 * -1nI + x * -1nI) = In(x + 2) + -1In(x + 3)
3nI + nxI + (1nI + -1nxI) = In(x + 2) + -1In(x + 3)

Reorder the terms:
3nI + 1nI + nxI + -1nxI = In(x + 2) + -1In(x + 3)

Combine like terms: 3nI + 1nI = 4nI
4nI + nxI + -1nxI = In(x + 2) + -1In(x + 3)

Combine like terms: nxI + -1nxI = 0
4nI + 0 = In(x + 2) + -1In(x + 3)
4nI = In(x + 2) + -1In(x + 3)

Reorder the terms:
4nI = nI(2 + x) + -1In(x + 3)
4nI = (2 * nI + x * nI) + -1In(x + 3)
4nI = (2nI + nxI) + -1In(x + 3)

Reorder the terms:
4nI = 2nI + nxI + -1nI(3 + x)
4nI = 2nI + nxI + (3 * -1nI + x * -1nI)
4nI = 2nI + nxI + (-3nI + -1nxI)

Reorder the terms:
4nI = 2nI + -3nI + nxI + -1nxI

Combine like terms: 2nI + -3nI = -1nI
4nI = -1nI + nxI + -1nxI

Combine like terms: nxI + -1nxI = 0
4nI = -1nI + 0
4nI = -1nI

Solving
4nI = -1nI

Solving for variable 'n'.

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

Add 'nI' to each side of the equation.
4nI + nI = -1nI + nI

Combine like terms: 4nI + nI = 5nI
5nI = -1nI + nI

Combine like terms: -1nI + nI = 0
5nI = 0

Divide each side by '5'.
nI = 0

Simplifying
nI = 0

The solution to this equation could not be determined.

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