# Solve for x x/(x+7)-7/(x-7)=(x^2+49)/(x^2-49)

Factor each term.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
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 positive 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 factor for is itself.
occurs time.
The factor for is itself.
occurs time.
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 .
Simplify each term.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Apply the distributive property.
Multiply by .
Move to the left of .
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Apply the distributive property.
Multiply by .
Subtract from .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Solve the equation.
Move all terms containing to the left side of the equation.
Subtract from both sides of the equation.
Combine the opposite terms in .
Subtract from .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Exclude the solutions that do not make true.
No solution
Solve for x x/(x+7)-7/(x-7)=(x^2+49)/(x^2-49)

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