Rational Expressions and Their Properties

The video tutorial explains how to divide rational expressions by multiplying by the reciprocal, similar to dividing fractions. It covers simplifying expressions by identifying common factors and determining the domain by excluding values that make the denominator zero. A second example is provided to reinforce these concepts, emphasizing the importance of factorization and domain determination.

What is the first step in dividing rational expressions?

• Divide the numerators

• Subtract the denominators

• Multiply by the reciprocal

• Add the numerators

When multiplying fractions, what should you do after multiplying the numerators and denominators?

• Divide the results

• Subtract the results

• Add the results

• Simplify the fraction

What is the prime factorization of 6x^2?

• 3 * 3 * x

• 2 * 2 * x

• 2 * 3 * x * x

• 2 * 3 * x

Why must zero be excluded from the domain of a rational expression?

• It makes the expression undefined

• It makes the denominator zero

• It makes the numerator zero

• It makes the expression negative

In the second example, what is the reciprocal of the fraction used?

• y^2 - 4y - 21 / 4y

• 4y / y^2 - 4y - 21

• y + 3 / 8y^2

• 8y^2 / y + 3

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

• 2(y + 3) / y^2

• 2(y - 7) / y^2

• y^2 / 2(y + 3)

• y^2 / 2(y - 7)

Which value must be excluded from the domain in the second example?

• y = 0

• y = 7

• All of the above

• y = -3

What is the factorization of y^2 - 4y - 21?

• (y - 7)(y - 3)

• (y + 3)(y + 7)

• (y - 7)(y + 3)

• (y - 3)(y + 7)

What is the domain of the simplified expression in the second example?

• All real numbers except 7

• All real numbers except -3, 0, and 7

• All real numbers except 0

• All real numbers

What is the common factor between the numerator and denominator in the second example?

• 8y^2

• y + 3

• y - 7

• y^2