Simplifying Rational Expressions: Key Techniques and Examples

Nancy explains how to simplify rational expressions by factoring the numerator and denominator, canceling common terms, and understanding restrictions. She provides examples, discusses the importance of noting conditions, and addresses common misconceptions. The video covers basic to advanced examples, including handling complex coefficients, and emphasizes the need to write restrictions when canceling factors.

What is the first step in simplifying a rational expression?

• Cancel common terms

• Factor the expression

• Identify the type of expression

• Solve for x

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CCSS.HSA.APR.D.6

What formula is used to factor expressions like x^2 minus a perfect square?

• Difference of squares

• Factor by grouping

• Sum of squares

• Quadratic formula

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CCSS.HSA.APR.C.4

What must you always check before simplifying a rational expression?

• If the expression is complete

• If there are any common terms to cancel

• If there are any restrictions on the variable

• If the denominator is zero

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CCSS.HSA.APR.D.6

What happens when you cancel a factor that makes the denominator zero?

• The expression becomes undefined

• It simplifies without restrictions

• A restriction is created

• The numerator becomes zero

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CCSS.HSF-IF.C.7D

Why is it important to note restrictions when simplifying rational expressions?

• To ensure the expression is defined for all real numbers

• To simplify the expression further

• To make the expression more complex

• To avoid division by zero

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CCSS.HSA.APR.D.6

What is a common mistake to avoid when canceling terms in a rational expression?

• Forgetting to simplify the constants

• Factoring incorrectly

• Ignoring the variable

• Canceling non-like terms

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CCSS.HSA.APR.D.6

How do you handle negative signs when factoring expressions?

• Multiply them through the expression

• Ignore them

• Factor them out with the constants

• Cancel them with positive terms

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CCSS.7.EE.A.1

What should you do if the coefficients are large in a rational expression?

• Estimate the factors

• Factor out the greatest common divisor

• Divide all terms by the largest coefficient

• Simplify the expression first

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CCSS.HSA.APR.D.6

What is the result of factoring and simplifying the expression 15x^2 - 90x + 120?

• 3x(5x - 30) + 120

• 3(5x^2 - 30x + 40)

• 5x(3x - 6) + 20

• Cannot be factored

What is the correct restriction for the expression after canceling the term (5x - 6)?

• x cannot equal six-fifths

• x cannot equal 6

• x cannot equal 1

• x cannot equal -6