Simplifying Rational Expressions and Excluded Values

The video tutorial covers simplifying rational expressions, focusing on identifying excluded values that make the denominator zero. It explains factoring techniques for polynomials and how to simplify expressions by canceling common factors. The tutorial also highlights common mistakes and provides advanced techniques for simplification, ensuring a comprehensive understanding of the topic.

What is an excluded value in a rational expression?

• A value that makes the fraction equal to one

• A value that makes the denominator zero

• A value that makes the numerator zero

• A value that makes the expression undefined

What is the first step in simplifying a rational expression?

• Subtracting the numerator from the denominator

• Factoring the numerator and denominator

• Adding the numerator and denominator

• Multiplying the numerator and denominator

What should you do if you have a common factor in the numerator and denominator?

• Multiply them together

• Cancel them out

• Add them together

• Divide them

When simplifying x^5 / x, what is the result?

• x

• x^6

• x^5

• x^4

In the expression 32 / 4, what is the simplified result?

• 8

• 4

• 32

• 16

What is the simplified form of 4(x + 4) / (x + 4)(x - 9)?

• 4(x + 4) / (x + 4)

• 4(x - 9) / (x + 4)

• 4(x + 4) / (x - 9)

• 4 / (x - 9)

What are the excluded values for the expression 4 / (x - 9)?

• x = 9

• x = -4

• x = -9

• x = 4

What is the simplified form of (x^2 - 25) / (8x - 40)?

• (x + 5) / 8

• (x + 5) / (x - 5)

• (x - 5) / 8

• (x - 5)(x + 5) / 8

What is a common mistake when simplifying rational expressions?

• Multiplying the numerator and denominator

• Adding the numerator and denominator

• Cancelling terms that are not factors

• Subtracting the numerator from the denominator

What is the simplified form of (x^2 - 49) / (x^2 - 9x + 14)?

• (x + 7) / (x - 2)

• (x - 7) / (x - 2)

• (x + 7) / (x + 2)

• (x - 7) / (x + 2)