Mastering Rational Expressions: Addition and Subtraction

What is the first step in adding or subtracting rational expressions?

• Factor the denominators

• Simplify the expressions

• Multiply the numerators

• Find the common denominator

What operation is performed first in the process?

• Subtraction

• Addition

• Division

• Multiplication

What must the common denominator include for the given rational expressions?

• The sum of all denominators

• The highest degree of x

• All unique factors from the denominators

• The product of all numerators

Which of the following is a difference of squares?

• x^2 - 25

• x + 5

• x^2 + 25

• 2x - 10

What must be true for the common denominator of rational expressions?

• It must be the product of the numerators

• It should exclude any factors common to all denominators

• It must include all factors from the original denominators

• It should be the simplest expression possible

How do you adjust the numerator when the denominator is multiplied by a new term?

• Add the new term to the numerator

• Subtract the new term from the numerator

• Multiply the numerator by the same new term

• Divide the numerator by the new term

What happens to the expression after simplifying the numerator and denominator?

• It remains unchanged

• It reduces to a simpler rational expression

• It simplifies to a single variable x

• It becomes undefined

What is the simplified form of the expression after finding a common denominator and adjusting numerators?

• x - 5 over 2

• 2 over x + 5

• 4(x - 5) over 2(x + 5)(x - 5)

• 2x - 20 over 2(x + 5)(x - 5)

Why is it important to consider the domain of the expression?

• To find the range of the function

• To simplify the expression further

• To identify values that make the denominator zero

• To ensure the expression is defined for all real numbers

What is the result of simplifying the given rational expressions?

• A single rational expression in simplest form

• A polynomial of degree 2

• A complex number

• An undefined expression