Rational Expressions and Their Properties

The video tutorial explains how to subtract two rational expressions by first factoring the denominators to find the least common denominator. It then demonstrates how to simplify the numerator after subtraction and further simplifies the expression by factoring. Finally, it identifies the values that must be excluded from the domain to avoid division by zero.

What is the first step in subtracting two rational expressions when they do not have a common denominator?

• Factor the denominators to find a common denominator.

• Multiply the expressions by each other.

• Ignore the denominators and subtract the numerators.

• Add the numerators directly.

How do you determine the least common denominator for two rational expressions?

• By multiplying the denominators together.

• By adding the denominators together.

• By finding the greatest common factor of the numerators.

• By factoring the denominators and identifying common factors.

Once a common denominator is found, what remains unchanged when subtracting two rational expressions?

• The entire expression.

• The denominators.

• The numerators.

• The coefficients of the terms.

What is the result of combining like terms in the expression x^2 - 2x + 9x - 8 + 20?

• x^2 + 7x - 12

• x^2 + 7x + 12

• x^2 + 11x + 12

• x^2 - 7x + 12

What is the purpose of factoring the numerator in a rational expression?

• To change the expression into a quadratic equation.

• To eliminate all terms in the numerator.

• To find common factors with the denominator for simplification.

• To increase the degree of the polynomial.

What is the simplified form of the expression after factoring out common terms?

• (x + 4) / (x + 2)

• (x + 3) / (x + 2)

• (x + 4) / (x - 2)

• (x + 3) / (x - 3)

Why must certain values of x be excluded from the domain of a rational expression?

• Because they are negative values.

• Because they make the denominator zero, leading to undefined expressions.

• Because they make the expression a complex number.

• Because they make the numerator zero.

Which values of x are excluded from the domain of the expression (x + 3)(x + 2) = 0?

• x = 3 and x = 2

• x = 3 and x = -2

• x = -3 and x = 2

• x = -3 and x = -2

What happens to the function f(x) at x = -3?

• It becomes zero.

• It becomes undefined due to division by zero.

• It remains unchanged.

• It becomes a complex number.

What is the factorization of the denominator of g(x) that leads to domain exclusions?

• (x + 3)(x - 2)

• (x - 3)(x - 2)

• (x + 3)(x + 2)

• (x - 3)(x + 2)