Rational Expressions and Their Domains

The video tutorial explains how to determine the domain and simplify rational expressions. It covers the process of identifying excluded values by setting the denominator equal to zero and factoring both the numerator and denominator to simplify expressions. Three examples are provided to illustrate these concepts, each demonstrating the step-by-step process of factoring, identifying common factors, and simplifying the expression while determining the domain.

What is the domain of a rational expression?

• All real numbers except those that make the denominator zero

• All real numbers

• All real numbers except those that make the numerator zero

• Only positive real numbers

Why do we exclude certain values from the domain of a rational expression?

• Because they make the expression positive

• Because they make the expression undefined

• Because they make the expression negative

• Because they make the expression zero

What is the simplified form of the expression 6x^4 / 24x^2?

• x^3 / 6

• x^2 / 6

• x^3 / 4

• x^2 / 4

What is the domain of the expression 6x^4 / 24x^2?

• All real numbers

• All real numbers except negative numbers

• All real numbers except one

• All real numbers except zero

What is the greatest common factor of the numerator in the expression 2x - 10?

• 2

• 1

• 5

• 10

Which values are excluded from the domain of the expression (2x - 10) / (x^2 - 2x - 15)?

• x = 0 and x = -3

• x = 0 and x = 5

• x = -3 and x = 5

• x = 3 and x = -5

What is the simplified form of the expression (2x - 10) / (x^2 - 2x - 15)?

• x / (x + 3)

• x / (x - 3)

• 2 / (x - 3)

• 2 / (x + 3)

What is the greatest common factor in the denominator of the expression x^3 - 7x^2 + 12x?

• 12

• x

• x^2

• 7

Which values are excluded from the domain of the expression (x^2 - x - 6) / (x^3 - 7x^2 + 12x)?

• x = 1, x = -3, and x = -4

• x = 1, x = 3, and x = 4

• x = 0, x = 3, and x = 4

• x = 0, x = -3, and x = -4

What is an alternative way to express the simplified form of (x^2 - x - 6) / (x^3 - 7x^2 + 12x)?

• (x - 2) / (x^2 - 4x)

• (x - 2) / (x^2 + 4x)

• (x + 2) / (x^2 + 4x)

• (x + 2) / (x^2 - 4x)