Solve for z (6z)/(z^2+4z-21)+7/(z+7)=1

Math
Factor using the AC method.
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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.
Find the LCD of the terms in the equation.
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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 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.
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Multiply each term in by in order to remove all the denominators from the equation.
Simplify .
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Simplify each term.
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Apply the distributive property.
Multiply by .
Add and .
Simplify .
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Multiply by .
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
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Simplify each term.
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Multiply by .
Move to the left of .
Multiply by .
Subtract from .
Solve the equation.
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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.
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Subtract from both sides of the equation.
Subtract from .
Move to the left side of the equation by adding it to both sides.
Combine the opposite terms in .
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Add and .
Add and .
Factor out of .
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Factor out of .
Factor out of .
Factor out of .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to .
Set the next factor equal to and solve.
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Set the next factor equal to .
Add to both sides of the equation.
The final solution is all the values that make true.
Solve for z (6z)/(z^2+4z-21)+7/(z+7)=1

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