Adding and Subtracting Rational Expressions Explained

This video tutorial covers the process of adding and subtracting rational expressions. It begins with an introduction to rational expressions, emphasizing the importance of common denominators. The video then provides three examples: simplifying fractions with common denominators, handling complex denominators, and factoring denominators to simplify expressions. The tutorial concludes with tips for simplifying rational expressions and encourages viewers to practice with basic fractions to reinforce the concepts.

What distinguishes a rational expression from a rational equation?

• The presence of a variable

• The type of numbers used

• The inclusion of an equal sign

• The complexity of the expression

What is the first step in solving rational expressions?

• Factoring the numerator

• Finding the common denominator

• Multiplying the expressions

• Simplifying the variables

What is necessary to add or subtract fractions with variables?

• Dividing the expressions

• Subtracting the denominators

• Finding the least common multiple

• Multiplying the numerators

How do you simplify 2/x + 3/x^2?

• 5/x^2

• 2x + 3/x^2

• 3x + 2/x

• 5/x^3

What is a common mistake to avoid when adding rational expressions?

• Forgetting to find the LCM

• Multiplying instead of adding

• Ignoring variable terms

• Factoring incorrectly

What is the least common multiple of (x + 2) and (x - 6)?

• 2x - 4

• x^2 + 2x - 6

• (x + 2)(x - 6)

• x^2 - 4x - 12

After simplifying, what is the result of adding x/(x+2) + 4x/(x-6)?

• 5x^2 + 2x/(x + 2)(x - 6)

• 5x^2 + 2x/(x^2 - 4x - 12)

• x^2 + 8x/(x^2 - 4x - 12)

• x + 4x/(x + 2)(x - 6)

What is the simplified form of (x - 1)/(x^2 + 5x + 6) - 5/(x + 3)?

• x - 1 - 5/(x + 3)

• -4x - 11/(x^2 + 5x + 6)

• x - 6/(x^2 + 8x + 9)

• -4x - 11/(x + 2)(x + 3)

Why is it important to factor denominators in rational expressions?

• To convert them into equations

• To increase the complexity

• To eliminate the variables

• To simplify the expression further

How do you handle negative signs when combining rational expressions?

• Distribute to all terms

• Ignore them

• Apply only to the denominator

• Apply only to the numerator