Rational Expressions and Their Properties

The video tutorial covers adding and subtracting rational expressions with like denominators. It includes two examples: one for addition and one for subtraction. The process involves identifying common denominators, combining numerators, simplifying expressions, and determining the domain by excluding values that make the denominator zero. The tutorial emphasizes the importance of factoring and using the original expression to find the domain.

What is the first step in adding or subtracting rational expressions?

• Divide the expressions

• Multiply the expressions

• Find a common denominator

• Find a common numerator

In the first example, what is the common denominator?

• x + 2

• x - 3

• x - 2

• x + 3

What is the greatest common factor of the numerator in the first example?

• 12

• 12x

• 36

• x + 3

What value of x is excluded from the domain in the first example?

• x = -2

• x = 3

• x = -3

• x = 2

In the second example, what operation is performed on the numerators?

• Division

• Subtraction

• Multiplication

• Addition

Why is it important to use parentheses when subtracting the numerators in the second example?

• To ensure the entire numerator is subtracted

• To simplify the expression

• To find the common denominator

• To factor the expression

What is the simplified form of the numerator in the second example?

• 3x - 2

• 7x + 5

• 4x + 5

• 7x - 4x

What value of x is excluded from the domain in the second example?

• x = -2

• x = 2

• x = -3

• x = 3

What is the result of distributing a negative one in the second example?

• It adds the terms

• It multiplies the terms

• It changes the signs of the terms

• It divides the terms

What is the final simplified form of the rational expression in the second example?

• 3x - 2

• 7x + 3

• 4x + 5

• 3x + 2