# Solve for x natural log of x+5 = natural log of x-1- natural log of x+1

Use the quotient property of logarithms, .
For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.
Solve for .
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Simplify the right side of the equation.
Simplify each term.
Split the fraction into two fractions.
Move the negative in front of the fraction.
Find the common denominator.
Write as a fraction with denominator .
Multiply by .
Multiply and .
Combine the numerators over the common denominator.
Simplify the numerator.
Apply the distributive property.
Multiply by .
Subtract from .
Subtract from .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Simplify with factoring out.
Factor out of .
Rewrite as .
Factor out of .
Simplify the expression.
Rewrite as .
Move the negative in front of the fraction.
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Find the LCD of the terms in the equation.
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
The LCM is the smallest number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
The factor for is itself.
occurs time.
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
Multiply each term by and simplify.
Multiply each term in by in order to remove all the denominators from the equation.
Simplify the left side of the equation by cancelling the common factors.
Cancel the common factor of .
Move the leading negative in into the numerator.
Cancel the common factor.
Rewrite the expression.
Apply the distributive property.
Multiply.
Multiply by .
Multiply by .
Simplify .
Apply the distributive property.
Simplify the expression.
Multiply by .
Multiply by .
Solve the equation.
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Move all terms containing to the left side of the equation.
Add to both sides of the equation.
Move to the left side of the equation by adding it to both sides.
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Set equal to and solve for .
Set the factor equal to .
Subtract from both sides of the equation.
Set equal to and solve for .
Set the factor equal to .
Subtract from both sides of the equation.
The solution is the result of and .
Exclude the solutions that do not make true.
No solution
Solve for x natural log of x+5 = natural log of x-1- natural log of x+1

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