Rational Expressions and Their Properties

This video tutorial covers the addition and subtraction of rational expressions with both like and unlike denominators. It begins with a basic introduction to the concept, followed by detailed steps and examples for handling expressions with like denominators. The tutorial then progresses to more complex scenarios involving unlike denominators, explaining the use of the least common denominator (LCD) to simplify the process. Throughout the video, various examples are provided to illustrate the concepts, along with simplification techniques and important notes on avoiding division by zero.

What remains unchanged when adding or subtracting rational expressions with like denominators?

• The numerator

• The denominator

• Both numerator and denominator

• Neither numerator nor denominator

Why can't the denominator be zero in rational expressions?

• It makes the expression negative

• It makes the expression zero

• It makes the expression infinite

• It makes the expression undefined

In the example 2/9 + 1/9, what is the simplified result?

• 1/3

• 3/9

• 1/9

• 2/3

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

• Add the numerators

• Find the least common denominator

• Subtract the numerators

• Simplify the expression

What is the least common denominator (LCD) for the fractions 1/30 and 5/12?

• 12

• 30

• 120

• 60

When finding the LCD, what should you do if a denominator is missing a factor?

• Ignore the missing factor

• Add the missing factor to the numerator

• Multiply the numerator and denominator by the missing factor

• Subtract the missing factor from the numerator

In the expression 15x - 14y, why can't it be simplified further?

• It is already in simplest form

• It has a common factor of one

• It has no common factors

• It is a complex expression

What should be noted before simplifying a rational expression?

• The expression should be negative

• The numerator should be zero

• The denominator should not be zero

• The expression should be positive

In the expression 6x - 2, what is the greatest common factor?

• 2

• 1

• 3

• 6

What is the simplified form of the expression 2(y + 8) / ((y - 4)(y + 2))?

• 2 / ((y - 4)(y + 2))

• y + 8

• y - 4

• 2(y + 8)