Rational Expressions and Factoring Concepts

The video tutorial explains how to divide rational expressions by converting division into multiplication using the reciprocal of the divisor. It emphasizes the importance of simplifying expressions by factoring before multiplying. The tutorial provides detailed examples of factoring quadratic expressions and simplifying them by canceling common factors. It concludes with a final multiplication of the simplified expressions, highlighting the importance of not simplifying across addition or subtraction.

What is the first step in dividing rational expressions?

• Divide the numerators directly

• Subtract the denominators

• Multiply by the reciprocal of the divisor

• Add the numerators

What is the reciprocal of a fraction?

• The fraction with numerator doubled

• The fraction with numerator and denominator interchanged

• The fraction itself

• The fraction with denominator doubled

What must be done before multiplying rational expressions?

• Add the expressions

• Divide the expressions

• Factor the expressions

• Subtract the expressions

Which of the following is a factor of x^2 - 4x - 12?

• x - 2

• x + 6

• x + 4

• x - 6

Which expression is a difference of squares?

• x^2 - 16

• x^2 - 4x - 12

• x^2 - 2x - 24

• x^2 + 4x + 4

What is the factorization of x^2 - 16?

• (x + 8)(x - 8)

• (x + 4)(x - 4)

• (x + 6)(x - 6)

• (x + 2)(x - 2)

What is the result of simplifying x + 4 over x + 4?

• 4

• x

• 0

• 1

What is the sum of the factors of -24 that add to -2?

• -6 and 4

• -4 and 6

• -12 and 2

• -8 and 3

Why can't we simplify across addition or subtraction?

• It changes the value of the expression

• It is not allowed in mathematics

• It is only possible with multiplication

• It is only possible with division

What happens when you multiply the simplified expressions?

• You get a simplified expression

• You get the original expression

• You get a larger expression

• You get an unsimplified expression