Exploring Adding and Subtracting Rational Expressions

What do you do with the numerators when adding rational expressions with the same denominator?

• Multiply them

• Subtract them

• Add them together

• Divide them

What must be true for two rational expressions to be added directly without finding an LCM?

• They must have polynomials as denominators

• They must have the same denominator

• They must have the same numerator

• They must have coefficients in the numerator

What happens to the denominators when adding rational expressions with like denominators?

• They are added together

• They are subtracted from each other

• They are multiplied together

• They remain unchanged

How do you find the least common multiple (LCM) of two polynomials?

• By multiplying the highest degree of each polynomial

• By adding the polynomials together

• By finding the product of their unique factors

• By subtracting one polynomial from the other

In the process of adding rational expressions with unlike denominators, what is the purpose of finding the LCM?

• To cancel out terms

• To create a common denominator

• To find the difference between expressions

• To simplify the numerators

What is the first step in adding rational expressions with unlike denominators?

• Cancel out similar terms

• Multiply the denominators

• Add the numerators directly

• Identify the least common multiple (LCM)

When subtracting rational expressions with unlike denominators, what must you do with the entire expression being subtracted?

• Ignore it as it cancels out

• Multiply it by the LCM

• Place it in parentheses before subtracting

• Divide it by the common denominator

What is the result of subtracting two rational expressions with unlike denominators after finding a common denominator?

• The difference of the numerators over the original denominators

• An expression with a new, unrelated denominator

• A simpler expression with the same denominator

• A compound fraction

What is a compound fraction?

• A fraction that contains one or more fractions in its numerator or denominator

• A fraction with a variable in the denominator

• A fraction that cannot be simplified further

• A fraction with a polynomial in the numerator

How do you simplify a compound fraction?

• By multiplying the denominators

• By converting it into a multiplication problem

• By finding the LCM of the inner fractions

• By combining the fractions into a single fraction