Simplifying Rational Expressions and Radicals

Professor Dave introduces rational expressions, emphasizing their importance in algebra. He explains how to simplify, multiply, divide, add, and subtract these expressions. The video covers techniques for handling complex rational expressions and removing radicals from denominators, ensuring students can manipulate these expressions effectively.

What is the first step in simplifying a rational expression?

• Subtract the denominators

• Add the numerators

• Multiply the denominators

• Factor the polynomials

When multiplying rational expressions, what should you do after factoring?

• Add the expressions

• Divide the expressions

• Cancel common terms

• Subtract the expressions

How do you handle division of rational expressions?

• Multiply by the reciprocal

• Add the numerators

• Subtract the denominators

• Factor the numerators

What is necessary to add or subtract rational expressions?

• A reciprocal

• A factorable expression

• A common denominator

• A common numerator

What method is used to combine the numerators when adding rational expressions?

• Reciprocal method

• Cross-multiplication

• Conjugate method

• FOIL method

How do you simplify a complex rational expression?

• Add the fractions directly

• Multiply by the reciprocal of the denominator

• Subtract the numerators

• Divide the denominators

What is the first step in simplifying a complex rational expression?

• Multiply the fractions in the denominator

• Subtract the denominators

• Combine the fractions in the numerator

• Add the numerators

How do you eliminate a radical in the denominator of a fraction?

• Multiply by the conjugate

• Add the radical

• Subtract the radical

• Multiply by the reciprocal

What happens when you multiply a radical by itself?

• The radical is eliminated

• The radical is halved

• The radical doubles

• The radical remains

What is the result of multiplying by the conjugate of a binomial with a radical?

• The radical is squared

• The radical is eliminated

• The radical is added

• The radical is subtracted