Mastering Multiplication and Division of Rational Expressions

What is a rational expression?

• An expression with variables in the denominator

• An expression with only constants

• An expression with variables in the numerator

• An expression with no variables

What is the first step in simplifying rational expressions?

• Dividing the terms

• Factoring the terms

• Multiplying the terms

• Adding the terms

Which of the following is a correct factorization of X^2 + 8X + 15?

• (X + 5)(X - 2)

• (X + 5)(X + 3)

• (X + 2)(X + 3)

• (X + 3)(X + 5)

What happens to common factors in the numerator and denominator?

• They are divided

• They are multiplied together

• They are added together

• They are canceled out

Why can't X - 2 and X + 2 be canceled out?

• They are constants

• They are not identical binomials

• They are in the numerator

• They are in the denominator

What is an excluded value?

• A value that makes the denominator zero

• A value that makes the numerator zero

• A value that makes the expression equal to one

• A value that makes the expression undefined

What is the excluded value for the factor X + 5?

• X = -5

• X = 5

• X = 10

• X = 0

What is the first step in dividing rational expressions?

• Keep the first fraction, change the operation to multiplication, and flip the second fraction

• Add the fractions

• Multiply the fractions directly

• Subtract the fractions

What is the final simplified form of 2(X - 1) / 3(X + 1)?

• 2(X - 1) / 3(X + 1)

• 2(X + 1) / 3(X - 1)

• 3(X - 1) / 2(X + 1)

• 3(X + 1) / 2(X - 1)

What are the excluded values for the expression 2(X - 1) / 3(X + 1)?

• X = 3, X = -3

• X = 1, X = -1

• X = 2, X = -2

• X = 0, X = 1