Rational Expressions and Functions

The video tutorial covers simplifying rational expressions and determining their domain. It begins by explaining the domain as the set of all x values that can be input into a function without making it undefined. The tutorial then demonstrates how to simplify a rational expression by factoring, specifically focusing on expressions of the form a^2 - b^2. It also addresses handling negatives in expressions, showing that a - b over b - a equals negative one. The video concludes with a simplified expression and emphasizes recognizing patterns in algebraic manipulation.

What is the first step in simplifying a rational expression?

• Identify the domain

• Subtract a constant

• Multiply by zero

• Add a constant

Which x value makes the function undefined?

• x = 0

• x = 6

• x = 1

• x = -6

What is the domain of the function?

• All real numbers

• All real numbers except -6

• All real numbers except 0

• All real numbers except 6

What is the form of the expression x^2 - 36?

• a^2 / b^2

• a^2 * b^2

• a^2 + b^2

• a^2 - b^2

How can x^2 - 36 be factored?

• (x + 6)(x - 6)

• (x - 6)(x + 6)

• (x + 6)(x + 6)

• (x - 6)(x - 6)

What is the relationship between x - 6 and 6 - x?

• They are equal

• They are reciprocals

• They are negatives of each other

• They are squares

What happens when you multiply x - 6 by -1?

• It becomes -x - 6

• It becomes x + 6

• It becomes 6 - x

• It becomes 6 + x

What is the simplified form of the expression after canceling terms?

• x + 6

• -x + 6

• -x - 6

• x - 6

What should you recognize about expressions like a - b over b - a?

• They are equal to a + b

• They are equal to -1

• They are equal to 0

• They are equal to 1

What is the general advice given for simplifying rational expressions?

• Ignore negative signs

• Always multiply by zero

• Recognize patterns like a - b over b - a

• Add constants to simplify