# Find Where Undefined/Discontinuous ((y^2-36)/y)÷((y+6)/(y-6))

Set the denominator in equal to to find where the expression is undefined.
Set the denominator in equal to to find where the expression is undefined.
Add to both sides of the equation.
Set the denominator in equal to to find where the expression is undefined.
Solve for .
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.
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 ((y^2-36)/y)÷((y+6)/(y-6))