# Solve by Factoring x/(x-3)+4/(x+3)=18/(x^2-9)

Move to the left side of the equation by subtracting it from both sides.
Simplify .
Simplify the denominator.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify the numerator.
Apply the distributive property.
Multiply by .
Move to the left of .
Apply the distributive property.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Subtract from .
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.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify the denominator.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify the numerator.
Apply the distributive property.
Multiply by .
Move to the left of .
Apply the distributive property.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Subtract from .
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.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
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 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.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Subtract from both sides of the equation.
Solve by Factoring x/(x-3)+4/(x+3)=18/(x^2-9)

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