Operations with Rational Expressions: Adding and Subtracting

This video tutorial covers operations with rational expressions, focusing on multiplication and division. It explains how to factor expressions, cancel common factors, and determine domain restrictions. The tutorial also includes error analysis and simplification techniques, emphasizing the importance of leaving answers in factored form to avoid mistakes.

What is the first step in multiplying irrational expressions?

• Combine like terms

• Solve for x

• Completely factor the expressions

• Identify the type of numbers involved

Which pairs of factors are used to cancel out terms in the given multiplication example?

• x - 2 and x + 2

• x + 3 and x + 3

• x + 2 and x - 2

• x + 3 and x - 3

What is the result of the multiplication in its factored form?

• x + 2 over x + 3 x - 3

• x - 2 over x - 3 x + 2

• x + 3 over x + 2 x - 2

• x - 3 over x - 2 x + 3

What values of x are excluded from the domain after factoring?

• -2, 2, -3

• -2, 2, 3

• 2, 3, -3

• -2, 2

How do you handle division of expressions differently from multiplication?

• Subtract the second expression from the first

• Multiply by the reciprocal of the second expression

• None of the above

• Add the expressions together

Which expression is flipped to the numerator during the division process?

• x - 1 * 3x + 1

• x + 2 x - 1

• x^2 + 1 * x + 2

• x * 3x + 1

What are the correct domain restrictions for the division example?

• x ≠ 0, 1/3, -2, 1

• x ≠ 0, -1/3, 2, -1

• x ≠ 0, -1/3, -2, 1

• x ≠ 0, -1/3, -2, -1

What common mistake is highlighted in the error analysis?

• All of the above

• Not setting the denominator not equal to zero

• Incorrectly factoring expressions

• Cancelling terms that should not be cancelled

What is the simplified expression from the error analysis?

• None of the above

• 53

• x - 7

• 5x - 35 over 3x - 21

What is the domain restriction from the error analysis?

• x ≠ 0

• x ≠ 1

• x ≠ -7

• x ≠ 7