Adding and Subtracting Rational Expressions Explained

What does 'rational' mean in the context of rational expressions?

• Relating to ratios

• Equations that equal zero

• Involving square roots

• Expressions with variables only

What is essential for adding or subtracting rational expressions?

• Different denominators

• Prime factorization of numerators

• Common denominators

• Multiplying denominators

How do you find the least common denominator for monomials?

• Multiply the coefficients

• Subtract the variables

• Use the highest exponents of each term

• Add the exponents

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

• Multiply the numerators

• Combine like terms

• Find the greatest common factor

• Factor each denominator completely

What do you do after factoring the denominators in polynomial rational expressions?

• Identify and add missing factors to each side

• Combine the expressions

• Simplify the numerator

• Divide by the common denominator

How do you simplify a rational expression after finding the common denominator?

• Cancel out like terms

• Combine and simplify the numerator

• Multiply the denominators

• Factor the numerator and denominator again

What must be true for two rational expressions to be added or subtracted?

• Their exponents must match

• Their numerators must be the same

• They must have the same variable

• They must have the same denominator

When factoring polynomial denominators, what is crucial to find?

• The sum of cubes

• The difference of squares

• The highest exponent

• The least common multiple

What is the result of simplifying a rational expression that involves subtraction?

• A difference of squares

• A polynomial in the numerator

• An undefined expression

• A single term in the numerator

How do you handle undefined situations in rational expressions?

• Ignore them

• Set the denominator equal to zero and solve

• Multiply them by the numerator

• Add them to the numerator