Exploring Adding and Subtracting Rational Expressions

The video tutorial introduces rational expressions, which are fractions with polynomials in the numerator and/or denominator. It outlines four steps for simplifying these expressions: factoring, simplifying using quotient rules, eliminating common factors, and writing the result. The tutorial covers simplifying monomial, binomial, and trinomial expressions, using techniques like GCF, difference of squares, and advanced factoring with coefficients.

What is a rational expression?

• An expression that only includes rational numbers

• A polynomial that includes a variable in the denominator

• A fraction where either numerator or denominator includes a polynomial

• A fraction where both numerator and denominator are integers

What is the first step in simplifying rational expressions?

• Apply the quotient rule

• Factor the numerator and the denominator

• Combine like terms

• Simplify the coefficients

How do you simplify the expression 12y over 48y^3?

• y/4y^2

• 1/4 y^2

• 3y/12y^2

• 4/12 y^3

What method is used to simplify the expression involving 8 and 24?

• Factoring out the greatest common factor

• Quotient rule

• None of the above

• Applying the power rule

What is the result when simplifying the expression with n plus 6 in both numerator and denominator?

• Undefined

• 1/3

• 3

• n + 6

What technique is applied to simplify the expression with a difference of squares?

• Applying the quotient rule

• Using the difference of squares method

• Simplifying coefficients

• Factoring out a common binomial

How is the trinomial in the numerator of example 11 factored?

• K^2 - 9K + 2

• K + 9 and K - 2

• K - 9 and K + 2

• K^2 + 9K - 2

What is the correct simplification after factoring and cancelling in example 17?

• 4M over M + 1

• M - 5 over M + 1

• 4 over M - 5

• M + 1 over 4M

In example 19, after cancelling X plus 1, what further simplification is needed?

• No further steps required

• Reduce 8/10 to 4/5

• Multiply numerator by 10

• Divide by X in the numerator

What is the final result for example 20 after all simplifications?

• Y - 4 over Y + 1

• 5Y - 2 over 10

• None of the above

• Y + 4 over Y - 1