Mastering Addition and Subtraction of Rational Expressions

This video tutorial covers the addition and subtraction of 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 unlike denominators, explaining the necessity of finding the least common denominator (LCD) and demonstrating the process through examples. Special cases, such as opposite denominators, are also addressed. The video concludes with a summary of key techniques and examples to reinforce learning.

How do you simplify a fraction with a common factor in the numerator and denominator?

• Multiply both by the common factor

• Divide both by the common factor

• Add the common factor to both

• Subtract the common factor from both

Why is it important to use parentheses when subtracting rational expressions?

• To ensure correct order of operations

• To decrease the value of the denominator

• To make the expression look neater

• To increase the value of the numerator

What is the first step in adding or subtracting rational expressions with unlike denominators?

• Combine the numerators

• Find the least common denominator

• Multiply the expressions

• Simplify the fractions

How do you determine the least common denominator of two rational expressions?

• By multiplying the denominators

• By adding the denominators

• By finding the highest exponent

• By factoring the denominators and including each factor the maximum number of times it appears

What is the purpose of factoring denominators in rational expressions?

• To reduce the fraction to its lowest terms

• To eliminate variables

• To find the LCD

• To simplify the expression

What do you multiply the numerator and denominator by when adjusting fractions to have the LCD?

• The original denominator

• Any missing factors from the LCD

• The least common multiple

• The highest common factor

When adding fractions with the LCD, what is the next step after rewriting them with common denominators?

• Subtract the fractions

• Add the fractions

• Factor the denominator

• Simplify the numerator

In the special case of opposite denominators, what operation is performed to make the denominators the same?

• Subtraction

• Division

• Addition

• Multiplication by -1

How does multiplying by -1 affect the terms in a rational expression with opposite denominators?

• It decreases the value of each term

• It leaves the terms unchanged

• It increases the value of each term

• It changes the sign of each term

What is the result of simplifying a difference of squares in rational expressions?

• A single variable

• A sum of two terms

• A product of two binomials

• An unchanged expression