Adding and Subtracting Rational Expressions with Like Denominators

The video tutorial explains how to add and subtract rational expressions by ensuring a common denominator. It covers the process of simplifying expressions by factoring numerators and denominators, and highlights the importance of identifying common factors to simplify results. The tutorial provides detailed examples for both addition and subtraction, emphasizing the need to distribute negative signs when subtracting. The lesson concludes with a simplified expression for each example.

What is required to add or subtract rational expressions?

• Different denominators

• Common denominators

• Same numerators

• Different numerators

What remains the same when adding rational expressions with like denominators?

• Numerator

• Denominator

• None of the above

• Both numerator and denominator

What is the first step in simplifying the numerator after adding rational expressions?

• Dividing the terms

• Multiplying the terms

• Dropping the parentheses

• Adding the denominators

What is the common factor in the trinomial x^2 + 8x + 12?

• 1

• 6

• 4

• 2

What are the binomial factors of x^2 + 8x + 12?

• (x + 5)(x + 2)

• (x + 6)(x + 2)

• (x + 4)(x + 3)

• (x + 6)(x + 3)

What happens to the common factor x + 6 in the numerator and denominator?

• It is subtracted

• It is simplified to 1

• It is added

• It is multiplied

What is the simplified sum of the first example?

• x + 12

• x + 8

• x + 2

• x + 6

What is the first step in subtracting rational expressions with a common denominator?

• Multiplying the numerators

• Distributing a negative one

• Adding the numerators

• Changing the denominator

What are the binomial factors of x^2 - 8x + 12?

• (x - 6)(x - 2)

• (x - 4)(x - 3)

• (x - 6)(x - 3)

• (x - 5)(x - 2)

What is the simplified difference of the second example?

• (x - 6)/(x + 2)

• (x - 2)/(x + 6)

• (x - 2)/(x + 3)

• (x - 3)/(x + 2)