Understanding Rational Numbers and Expressions

This video tutorial introduces rational expressions, explaining their definition and providing examples. It covers when rational expressions are undefined due to division by zero and demonstrates how to graph them, highlighting asymptotes. The tutorial also teaches how to simplify rational expressions by factoring and canceling common factors, with several examples to illustrate these concepts.

What is a rational number?

• A number that cannot be expressed as a fraction.

• A number that can be expressed as the quotient of two integers with a non-zero denominator.

• A number that is always positive.

• A number that is always negative.

Which of the following is an example of a rational number?

• e

• Pi

• 3/4

• Square root of 5

How can every integer be expressed as a rational number?

• By adding 1 to it

• By subtracting 1 from it

• By multiplying it by 2

• By writing it over 1

What is a rational expression?

• A polynomial with no variables

• The quotient of two polynomials with a non-zero denominator

• A single polynomial

• A polynomial with a zero denominator

Which of the following is a rational expression?

• x^2 - 1

• 3x - 4 / (x^2 - 1)

• x^2 + 5

• 3x - 4

When is a rational expression undefined?

• When the numerator is zero

• When the denominator is zero

• When both numerator and denominator are zero

• When the expression is negative

How do you determine the values that make a rational expression undefined?

• Set the numerator equal to zero

• Set the denominator equal to zero

• Set both numerator and denominator equal to zero

• Set the expression equal to one

What is the first step in simplifying a rational expression?

• Divide the numerator by the denominator

• Factor the numerator and denominator completely

• Add the numerator and denominator

• Multiply the numerator and denominator

Which of the following is a common mistake when simplifying rational expressions?

• Canceling common factors

• Factoring the numerator

• Canceling terms that are not factors

• Multiplying the numerator and denominator

What should you do after factoring the numerator and denominator of a rational expression?

• Add them together

• Subtract them

• Multiply them

• Cancel any common factors