Understanding Rational Expressions and Domains

The video tutorial explains how to subtract fractions by first factoring the denominators to find a common denominator. It then demonstrates the subtraction process and simplifies the resulting expression by combining like terms. Finally, it discusses how to determine the domain of the rational expression by identifying values that make the denominator zero.

Why is it necessary to factor the denominators when subtracting rational expressions?

• To simplify the numerators

• To find the least common denominator

• To eliminate the denominators

• To add the expressions

What is the least common denominator for the expressions in the example?

• x^2 + 11x + 18

• x - 4 * x + 2

• x + 2

• x - 4

How do you rewrite a fraction to have a common denominator?

• Divide the numerator by the denominator

• Subtract the same value from the denominator

• Multiply the numerator and denominator by the necessary factor

• Add the same value to the numerator

What is the result of distributing a negative sign across a binomial?

• The signs of the terms are reversed

• The signs of the terms remain unchanged

• The terms are multiplied by zero

• The terms are added together

What is the greatest common factor of the numerator in the simplified expression?

• 12

• 6

• 3

• 2

What happens to common factors in the numerator and denominator of a rational expression?

• They are ignored

• They are canceled out

• They are added together

• They are multiplied

What is the simplified form of the rational expression after canceling common factors?

• x - 4

• x + 2

• 6 / (x - 4)

• 6 / (x + 2)

Why is it important to use the unsimplified denominator when determining the domain?

• To find the greatest common factor

• To ensure all possible values are included

• To simplify the expression further

• To exclude values that make the denominator zero

Which values are excluded from the domain of the expression?

• x = -2 and x = 4

• x = 2 and x = -4

• x = 3 and x = -3

• x = 0 and x = 1

What is the domain of the rational expression in the example?

• All negative numbers

• All positive numbers

• All real numbers except -2 and 4

• All real numbers