Simplifying Rational Functions Through Factoring

This video tutorial explains how to simplify rational functions, which are essentially fractions. It begins with basic fraction simplification and progresses to simplifying rational functions with variables. The tutorial covers factoring techniques and addresses more complex functions, emphasizing the importance of considering domain restrictions during simplification. The video concludes by highlighting the need to maintain domain constraints even after simplification.

What is a rational function?

• A function that involves only multiplication and division

• A function that is a fraction

• A function that is always positive

• A function that involves only addition and subtraction

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How do you simplify the fraction 8/12?

• Multiply both numerator and denominator by 4

• Divide both numerator and denominator by 4

• Multiply both numerator and denominator by 2

• Divide both numerator and denominator by 2

When simplifying 2X + 6 over 2X + 10, what common factor can be factored out?

• 3

• X

• 2

• 6

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After factoring out the common term in 2X + 6 over 2X + 10, what is the simplified form?

• X + 3 over X + 5

• X + 3 over 2X + 5

• X + 3 over 2X + 10

• 2X + 3 over X + 5

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What is the first step in simplifying the function 2x^2 - 6x - 20 / 2x^2 - 50?

• Multiply both numerator and denominator by 2

• Factor out the common term 2

• Add 6 to both numerator and denominator

• Subtract 6 from both numerator and denominator

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What does the numerator factor to in the function 2x^2 - 6x - 20?

• x - 5 and x + 2

• x - 3 and x + 2

• x - 5 and x + 5

• x + 5 and x + 2

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What does the denominator factor to in the function 2x^2 - 50?

• x + 5 and x + 2

• x - 5 and x + 5

• x - 5 and x + 2

• x - 3 and x + 2

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What is the simplified form of the function 2x^2 - 6x - 20 / 2x^2 - 50?

• x - 2 over x + 5

• x - 5 over x + 2

• x + 5 over x - 2

• x + 2 over x + 5

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What is the domain restriction for the simplified function x + 2 over x + 5?

• x ≠ -5

• x ≠ 2

• x ≠ -2

• x ≠ 5

What additional restriction must be considered from the initial function 2x^2 - 6x - 20 / 2x^2 - 50?

• x ≠ 5

• x ≠ 2

• x ≠ -5

• x ≠ -2

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