Find Where Undefined/Discontinuous ((3z^2-21z)/(6z+8))÷((z^3-14z^2+49z)/(15z+20))

Math
Set the denominator in equal to to find where the expression is undefined.
Solve for .
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Subtract from both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify .
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Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Set the denominator in equal to to find where the expression is undefined.
Solve for .
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Subtract from both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify .
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Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Set the denominator in equal to to find where the expression is undefined.
Solve for .
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Factor each term.
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Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor using the perfect square rule.
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Rewrite as .
Check the middle term by multiplying and compare this result with the middle term in the original expression.
Simplify.
Factor using the perfect square trinomial rule , where and .
Factor out of .
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Factor out of .
Factor out of .
Factor out of .
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.
Since has no factors besides and .
is a prime 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.
The Least Common Multiple of some numbers is the smallest number that the numbers are factors of.
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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Rewrite using the commutative property of multiplication.
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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Cancel the common factor.
Rewrite the expression.
Simplify .
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Apply the distributive property.
Multiply.
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Multiply by .
Multiply by .
Multiply by .
Solve the equation.
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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 .
Set the equal to .
Add to both sides of the equation.
The final solution is all the values that make true.
The equation is undefined where the denominator equals , the argument of a square root is less than , or the argument of a logarithm is less than or equal to .
Find Where Undefined/Discontinuous ((3z^2-21z)/(6z+8))÷((z^3-14z^2+49z)/(15z+20))


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