Rational Expressions and Simplification

The video tutorial explains how to add or subtract rational expressions by ensuring they have like denominators. It demonstrates the process through two examples, focusing on factoring denominators, simplifying expressions, and finding common denominators. The tutorial emphasizes the importance of not simplifying across addition and provides tips for recognizing and handling common factors.

What is the first step when adding or subtracting rational expressions with different denominators?

• Multiply the numerators

• Add the denominators

• Factor the denominators

• Subtract the numerators

In the first example, what type of expression is x^2 - 16?

• Sum of cubes

• Difference of squares

• Quadratic trinomial

• Linear binomial

After simplifying the first example, what is the common denominator?

• x + 4

• 3x + 4

• x^2 - 16

• x - 4

Why can't the 4 in the numerator and denominator be simplified in the first example?

• They are in different fractions

• They are not like terms

• They are part of an addition

• They are part of a subtraction

In the second example, what are the factors of x^2 that are used?

• x and 1

• x and 7

• x and x

• x and 6

What is the purpose of multiplying the denominator by x + 6 in the second example?

• To factor the numerator

• To simplify the expression

• To change the numerator

• To find a common denominator

What operation is performed after finding a common denominator in the second example?

• Multiplication of denominators

• Division of numerators

• Subtraction of numerators

• Addition of numerators

What is the greatest common factor used to simplify the numerator in the second example?

• -3

• 6

• 3

• 1

What indicates that the expression is in its simplest form in the second example?

• The numerator is zero

• There are no common factors between numerator and denominator

• The denominator is one

• The expression is a single fraction

What is the final result of the second example?

• -3x - 24

• x - 4

• -3(x + 8)

• x + 8