Rational Expressions and Their Operations

The video tutorial explains how to add and subtract rational expressions by ensuring they have like denominators. It begins with an introduction to the concept, followed by two examples. The first example demonstrates adding rational expressions by factoring denominators and finding a common denominator. The second example illustrates subtracting rational expressions using similar steps. The tutorial emphasizes the importance of factoring and maintaining common denominators to simplify expressions.

What is the first step when adding or subtracting rational expressions with different denominators?

• Subtract the numerators

• Factor the denominators

• Multiply the numerators

• Add the denominators

In the first example, what is the greatest common factor that is factored out from the denominator?

• 2X

• X

• 7

• X + 2

Why do we multiply the numerator and denominator by the same factor when adjusting denominators?

• To make the numerator larger

• To simplify the fraction

• To keep the fraction equivalent

• To change the value of the fraction

What is the common denominator in the first example after adjustments?

• 2X

• X squared times (X + 2)

• X squared

• X + 2

Why can't we simplify across addition or subtraction in rational expressions?

• It makes the expression more complex

• It changes the value of the expression

• It is not allowed in mathematics

• It is unnecessary

In the second example, what are the factors of -3 that add up to +2?

• +3 and +1

• +1 and -3

• +2 and -1

• +3 and -1

What additional factor is needed for the second fraction in the second example to have a common denominator?

• X + 3

• X squared

• X - 1

• X + 4

What is the result of combining the numerators in the second example?

• 48 + 12

• 12X - 12X

• 0 and 60

• 12X + 60

What is the purpose of distributing a negative sign in the second example?

• To factor the expression

• To correctly subtract the terms

• To simplify the expression

• To change the sign of the entire expression

What is the final result of the second example?

• 12X + 48

• 48 + 12

• 0

• 60