Simplifying Rational Expressions and Factors

The video tutorial explains how to simplify rational expressions by identifying and factoring out common factors in the numerators and denominators. It emphasizes the importance of not simplifying across addition or subtraction. The tutorial provides two examples: the first involves factoring a monomial and simplifying, while the second involves factoring trinomials into binomials. The video concludes with simplified forms of the expressions, highlighting the process of identifying common factors and ensuring correct simplification.

What is the first step in simplifying a rational expression?

• Add the numerators and denominators

• Factor the numerators and denominators

• Multiply the numerators and denominators

• Subtract the numerators from the denominators

In the first example, what common factor is factored out from the denominator?

• 3XY

• X^2Y

• 2XY

• 6XY

Why can't the 2's in the expression 2Y/Y - 2 be simplified?

• Because they are in different terms

• Because they are part of a subtraction

• Because they are in the numerator

• Because they are not common factors

What type of expressions are the numerator and denominator in the second example?

• Polynomials

• Trinomials

• Monomials

• Binomials

What are the factors of +12 that add up to -8 in the second example?

• -3 and -4

• -2 and -6

• -6 and -2

• -4 and -3

Why is it important to resist simplifying terms across addition or subtraction?

• It changes the value of the expression

• It is unnecessary

• It makes the expression more complex

• It is mathematically incorrect

What are the factors of -18 that add up to -3 in the second example?

• -3 and +6

• -9 and +2

• -6 and +3

• -2 and +9

What common factor is shared by the numerator and denominator in the second example?

• X + 6

• X - 6

• X - 2

• X + 3

What is the simplified form of the second example's rational expression?

• X - 2/X - 6

• X + 3/X - 2

• X - 2/X + 3

• X + 6/X - 3

What is the final step in simplifying a rational expression?

• Rewriting the expression

• Canceling out common factors

• Multiplying the remaining terms

• Adding the remaining terms