Rational Expressions and Denominators

This video tutorial covers the process of adding and subtracting rational expressions. It begins with a review of operations with like denominators, emphasizing the simplicity of adding or subtracting numerators. The tutorial then progresses to handling unlike denominators, introducing the concept of the least common denominator (LCD) and demonstrating how to factor denominators to find the LCD. Several examples illustrate these concepts, including special cases where denominators are opposites. The video concludes with a summary of the techniques and simplifications involved in these operations.

What is the first step in adding fractions with like denominators?

• Add the numerators

• Multiply the denominators

• Divide the numerators

• Subtract the numerators

When subtracting rational expressions, why is it important to use parentheses?

• To add the numerators

• To multiply the denominators

• To ensure the entire numerator is subtracted

• To simplify the expression

What must be done first when adding rational expressions with unlike denominators?

• Subtract the denominators

• Find the least common denominator

• Multiply the numerators

• Add the numerators directly

How do you determine the least common denominator (LCD) for rational expressions?

• By subtracting the numerators

• By analyzing the prime factors of the denominators

• By multiplying the numerators

• By adding the denominators

In the example with denominators 30 and 12, what is the least common denominator?

• 60

• 30

• 12

• 24

What is the result of adding 2/60 and 5/60?

• 2/60

• 5/60

• 7/60

• 3/60

When dealing with variables, how do you ensure the LCD includes all necessary factors?

• By adding extra variables

• By ignoring the variables

• By ensuring each variable is repeated the maximum number of times it appears

• By subtracting variables

In the advanced example, what is the result of simplifying M^2 - 9?

• M^2 - 3

• M^2 + 9

• (M + 3)(M - 3)

• M + 9

How do you handle denominators that are opposites, such as A + M and A - M?

• Add them directly

• Multiply by -1 to change the sign

• Subtract them directly

• Ignore the difference

What is the final simplified form of the expression M^2 - 9?

• M + 3

• M - 3

• M^2 - 9

• M + 9