# Solve for n (4n+8)/(n^2+n-72)+8/(n^2+n-72)=1/(n+9)

Factor out of .

Factor out of .

Factor out of .

Factor out of .

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.

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.

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 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 .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Add and .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move all terms containing to the left side of the equation.

Subtract from both sides of the equation.

Subtract from .

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

Subtract from .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

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