Simplifying Rational Expressions and Domains

The video tutorial explains the process of factoring numerators and denominators in algebraic expressions. It emphasizes the importance of the division property, which allows terms to be divided only when separated by multiplication. The tutorial also covers the simplification of expressions and highlights the significance of domain restrictions, noting that certain values make the denominator zero and must be excluded.

What is the first step in simplifying a rational expression?

• Add the numerator and denominator

• Factor the numerator and denominator

• Subtract the numerator from the denominator

• Multiply the numerator and denominator

Why can't we directly cancel out x squared terms in a rational expression?

• Because they are not separated by multiplication

• Because they are in the denominator

• Because they are not like terms

• Because they are in the numerator

In the expression (4 + 3) / (5 + 3), why can't we simplify it to 4/5?

• Because 4 and 5 are not equal

• Because addition is involved

• Because subtraction is involved

• Because multiplication is involved

When can the division property be applied to simplify expressions?

• When terms are divided

• When terms are separated by multiplication

• When terms are subtracted

• When terms are added

What is the result when a term is divided by itself?

• Infinite

• Undefined

• One

• Zero

Which operation allows for the cancellation of terms in a rational expression?

• Addition

• Subtraction

• Multiplication

• Division

What is the factored form of x^2 - 3x + 2?

• (x + 1)(x + 2)

• (x + 2)(x - 1)

• (x - 1)(x - 2)

• (x - 2)(x + 1)

Why is it tempting to cancel terms after factoring?

• Because they are in the numerator

• Because they look similar

• Because they are different

• Because they are in the denominator

What is the purpose of factoring in simplifying rational expressions?

• To add terms

• To multiply terms

• To subtract terms

• To identify common factors

What is the simplified form of (x - 2)(x - 1) / (x + 3)(x + 1)?

• (x - 2)(x - 1)

• Cannot be simplified further

• (x - 1)/(x + 1)

• (x - 2)/(x + 3)