Rational Expressions and Functions

The video tutorial explains how to add two rational expressions, focusing on finding a common denominator, simplifying the numerator, and determining excluded values from the domain. It begins with factoring the denominators to find the least common denominator, then adds the expressions and simplifies the result. The tutorial concludes by identifying values that must be excluded from the domain to avoid division by zero.

What is the first step in adding two rational expressions?

• Subtract the denominators

• Find a common denominator

• Divide the expressions

• Multiply the numerators

Why is it necessary to factor the denominators of rational expressions?

• To add the numerators

• To multiply the expressions

• To find the least common denominator

• To simplify the numerators

What is the result of distributing 2x in the expression 2x(x + 1)?

• 2x + 1

• 2x^2 + 2x

• 2x^2 + x

• x^2 + 2x

After combining like terms, what is the simplified form of the numerator 2x^2 + 2x + 11x + 21?

• 2x^2 + 2x + 21

• 2x^2 + 13x + 11

• 2x^2 + 11x + 21

• 2x^2 + 13x + 21

What is the common factor between the numerator and denominator in the expression 2x^2 + 13x + 21?

• x + 1

• 2x + 1

• 2x + 7

• x + 3

What is the simplified form of the sum function after factoring and canceling common factors?

• (2x + 7)/(x + 1)

• (x + 3)/(x + 1)

• (x + 1)/(x + 3)

• (x + 3)/(2x + 7)

Why must certain values of x be excluded from the domain of the sum function?

• To simplify the expression

• To ensure positive results

• To prevent division by zero

• To avoid negative results

Which value of x makes the denominator of the sum function zero?

• x = 0

• x = 2

• x = -1

• x = 1

What is another reason for excluding x = -7/2 from the domain?

• It is not a real number

• It simplifies the expression

• It makes the denominator of f(x) zero

• It makes the numerator zero

What is the factored form of the denominator of g(x)?

• (2x + 7)(x + 1)

• (x + 3)(x + 1)

• (2x + 1)(x + 3)

• (x + 7)(x + 1)