Rational Expressions and Domain Exclusions

The video tutorial explains how to add rational expressions and determine their domain. It begins by identifying the need for a common denominator and demonstrates how to find the least common denominator (LCD) by examining the factors of the denominators. The tutorial then shows how to convert the fractions to equivalent fractions with the LCD, add the numerators, and simplify the resulting expression. Finally, it discusses how to determine the domain by identifying values that make the denominator zero, concluding that the domain is all real numbers except zero.

What is the first step in adding rational expressions?

• Multiply the numerators

• Subtract the denominators

• Find a common denominator

• Divide the fractions

What is the prime factorization of 12?

• 2 x 6

• 2 x 2 x 3

• 2 x 3

• 3 x 4

Which factor is missing from the LCD when considering the second denominator?

• Factor of 2

• Factor of 3

• Factor of 5

• Factor of x

What do you multiply the numerator and denominator of the first fraction by to achieve the common denominator?

• 2x

• 3

• 5

• 4x

What is the result of adding the numerators 25y and 8xy?

• 33y

• 25y + 8xy

• 25xy + 8y

• 33xy

What common factor can be factored out from the numerator 25y + 8xy?

• 5

• y

• x

• 8

What is the simplified form of the expression 25y + 8xy over 60x squared?

• y(25x + 8) / 60x^2

• 25y / 60x^2

• 8xy / 60x^2

• y(25 + 8x) / 60x^2

What value of x is excluded from the domain of the expression?

• x = 1

• x = 5

• x = 0

• x = -1

Why is x = 0 excluded from the domain?

• It makes the expression negative

• It makes the expression undefined

• It makes the denominator zero

• It makes the numerator zero

How is the domain of the expression typically indicated?

• x cannot be zero

• x must be positive

• x can be any number

• x must be negative