Simplifying Rational Expressions and Factoring

In this video, the teacher explains how to simplify a rational expression by breaking it into two parts: the numerator and the denominator. The numerator is factored using the greatest common factor (GCF), while the denominator is factored by finding two numbers that multiply to a specific value and add to another. After factoring both parts, the expression is simplified by canceling out common factors, resulting in a simplified rational expression.

What is the first step in simplifying a rational expression?

• Break it into numerator and denominator

• Multiply the numerator and denominator

• Combine the numerator and denominator

• Add the numerator and denominator

What is the greatest common factor (GCF) of the numerator x^2 + 3x?

• 3

• x^2

• x

• x + 3

After factoring out the GCF from the numerator, what expression is left?

• x + 3

• x^2

• x(x + 3)

• x^2 + 3

Which pair of numbers multiply to -12 and add to -1?

• -4 and 3

• -3 and 4

• 2 and -6

• 1 and -12

What is the factored form of the denominator x^2 - x - 12?

• (x - 3)(x + 4)

• (x - 4)(x + 3)

• (x + 3)(x - 4)

• (x + 4)(x - 3)

What common factor can be canceled from the numerator and denominator?

• x - 4

• x

• x^2

• x + 3

What is the simplified form of the rational expression?

• x / (x + 3)

• 1 / (x - 4)

• x + 3 / x

• x / (x - 4)

What is the final step in simplifying a rational expression?

• Divide the numerator by the denominator

• Cancel out common factors

• Multiply the numerator and denominator

• Add the numerator and denominator