Simplifying Rational Expressions in Advanced Algebra

The video tutorial introduces rational expressions and functions, focusing on simplifying fractions by identifying common factors. It explains the importance of understanding the difference between terms and factors to avoid common mistakes in simplification. The tutorial progresses to simplifying expressions with variables, emphasizing the need for a strong foundation in numerical simplification. Advanced techniques such as using the greatest common factor (GCF) and factoring are demonstrated, particularly in the context of quadratic expressions. The tutorial aims to build a reliable foundation for working with more complex expressions involving variables.

What is a rational expression?

• A polynomial equation

• An integer divided by an integer

• A variable multiplied by a constant

• A subtraction of two numbers

Why can the fraction 4/10 be simplified?

• It has different numerators

• It cannot be simplified

• It has a common factor in the numerator and denominator

• It is a prime number

What does it mean to factor a number?

• Add several numbers together

• Divide it by another number

• Find its square root

• Break it down into smaller components that multiply to the original number

What is the simplified form of the expression (X+2)/(X+2)(X+1)?

• X+1

• 1/(X+1)

• X+2

• X^2+3X+2

In the expression (2+3)/3, why can't the threes be cancelled out?

• All of the above

• Because they are not factors

• Because they are in different expressions

• Because they are added, not multiplied

What remains in the numerator when (X+2) is cancelled in the expression (X+2)/(X+2)(X+1)?

• 1

• 0

• X+2

• X+1

What is the result of simplifying the expression 6x^2/(3x-9)?

• 2x^2/(x-3)

• 2x^2

• x^2-3

• Cannot be simplified

What is the simplified form of the expression with numerator 6x^2 and denominator 3x-9?

• x^2-3

• Cannot be simplified

• 2x^2/(x-3)

• 2x^2

Which method is not a factoring strategy discussed?

• Division method

• Difference of squares

• Greatest common factor

• Add multiply method

Which pair of numbers adds to -1 and multiplies to -6, useful in factoring X^2 - X - 6?

• 2 and -3

• 3 and -2

• 6 and -1

• 1 and -6