Adding and Subtracting Rational Expressions in Algebra II

This video tutorial by Kirk Weiler covers Unit 10, Lesson 8 of Common Core Algebra 2, focusing on combining rational expressions through addition and subtraction. The lesson begins with a review of basic fraction rules, emphasizing the need for a common denominator. It progresses to exercises that demonstrate how to combine and simplify fractions with variables, highlighting the importance of factoring. The tutorial also addresses subtraction of fractions, detailing the distribution of subtraction across terms. The session concludes with complex exercises and a summary of key skills developed.

What is the primary rule for adding or subtracting fractions?

• Subtraction is not allowed for fractions.

• Denominators must be the same.

• Numerators must be multiplied.

• Fractions must have different denominators.

How can denominators be changed when combining fractions?

• By adding constants.

• By multiplying the fraction by one.

• By dividing the fraction.

• By subtracting variables.

When combining rational expressions, what is the first step?

• Combine the numerators.

• Factor the numerator.

• Simplify the denominators.

• Find a common denominator.

Why is adding and subtracting rational expressions considered difficult?

• Because it involves division.

• It's actually considered easy.

• Because it requires memorization.

• Due to the complexity of finding common denominators.

What is the result of combining 4x/12x and 8x/12x?

• 14x-11/12x

• 12x^2/144x^2

• 12x/24x

• 22x/12x

Why is it important not to multiply out the denominators when combining fractions?

• To avoid changing the value.

• To simplify the calculation.

• Because it's mathematically incorrect.

• To keep the denominator factored for potential simplification.

How do you simplify a fraction with a numerator that cannot be factored?

• It's already in simplest form.

• By dividing the numerator and denominator by the same number.

• By adding a constant to both numerator and denominator.

• By factoring the denominator only.

What happens if you cannot factor the numerator in a rational expression?

• You must use a different method.

• The expression cannot be simplified.

• You should multiply the numerator by the denominator.

• The expression is undefined.

What is a common mistake when distributing subtraction across the numerator?

• Adding instead of subtracting.

• Distributing to the denominator instead.

• Forgetting to distribute to all terms.

• Multiplying the terms.

What is the result of subtracting 1 over X from 1 divided by (X minus 1)?

• (X - 1) - X

• 1 - X

• X/(X - 1)

• 1/(X^2 - X)