Simplifying Rational Expressions

The video tutorial covers simplifying rational expressions by factoring. It begins with an introduction and setup of two problems, followed by detailed solutions. The first problem involves factoring a difference of squares, while the second requires factoring both the numerator and denominator. Additional problems are introduced for practice, with solutions provided. The video concludes with an explanation of when a fraction is considered prime, meaning it cannot be simplified further.

What is the first step in simplifying the expression x + 9 over x^2 - 81?

• Factor the numerator

• Factor the denominator

• Combine like terms

• Expand the expression

How do you factor the denominator x^2 - 81?

• (x + 81)(x - 81)

• (x - 9)(x - 9)

• (x + 9)(x + 9)

• (x + 9)(x - 9)

What is the simplified form of the expression x + 9 over x^2 - 81?

• x / (x + 9)

• 1 / (x + 9)

• x / (x - 9)

• 1 / (x - 9)

What is the first step in simplifying the expression x^2 + 11x + 24 over x^2 + 4x - 32?

• Factor the numerator

• Factor the denominator

• Expand the expression

• Combine like terms

Which pair of factors correctly represents x^2 + 11x + 24?

• (x + 7)(x + 3)

• (x + 8)(x + 3)

• (x + 12)(x - 2)

• (x + 6)(x + 4)

What is the simplified form of the expression x^2 + 11x + 24 over x^2 + 4x - 32?

• (x + 8) / (x - 4)

• (x + 3) / (x - 4)

• (x + 3) / (x + 4)

• (x + 8) / (x + 4)

What is the first step in simplifying the expression x^2 - 4 over x^2 + 8x + 12?

• Factor the numerator

• Factor the denominator

• Combine like terms

• Expand the expression

Which pair of factors correctly represents x^2 - 4?

• (x + 2)(x - 2)

• (x - 2)(x - 2)

• (x + 2)(x + 2)

• (x + 4)(x - 4)

What is the simplified form of the expression x^2 - 4 over x^2 + 8x + 12?

• (x - 2) / (x - 6)

• (x + 2) / (x - 6)

• (x + 2) / (x + 6)

• (x - 2) / (x + 6)

What should you write if a fraction cannot be simplified further?

• Lowest terms

• Prime

• Irreducible

• Simplified