Algebra II

Advanced algebraic concepts including polynomials, rational expressions, and complex numbers.

Polynomials and Their PropertiesFactoring and Solving Polynomial EquationsRational Expressions and Equations
Complex Numbers and Their OperationsPolynomial Division and the Remainder TheoremPolynomial and Rational Inequalities
Modeling Real-World Data with PolynomialsApplications of Rational Expressions in Science and EngineeringComplex Numbers in Electrical Engineering and Art
Mastering Word ProblemsChecking Your SolutionsSmart Use of Calculators and Technology
Polynomials and Thei...Factoring and Solvin...Rational Expressions...Complex Numbers and ...Polynomial Division ...Polynomial and Ratio...Modeling Real-World ...Applications of Rati...Complex Numbers in E...Mastering Word Probl...Checking Your Soluti...Smart Use of Calcula...
Basic Concepts

Rational Expressions and Equations

What Are Rational Expressions?

Rational expressions are fractions where both the numerator and the denominator are polynomials. They look like \( \frac{x + 2}{x - 1} \).

Simplifying and Operations

  • Simplify: Cancel out common factors in the numerator and denominator.
  • Add/Subtract: Find a common denominator before combining.
  • Multiply/Divide: Multiply straight across, but remember to factor first for easier cancellation.

Solving Rational Equations

Set the rational expression equal to a number or another rational expression, clear denominators, and solve the resulting equation.

Watch Out!

Check for restrictions: denominators can never be zero.

Examples

  • \( \frac{x^2 - 4}{x - 2} = \frac{(x + 2)(x - 2)}{x - 2} = x + 2 \) (for \( x eq 2 \))

  • To solve \( \frac{2}{x} = 4 \), multiply both sides by \( x \) to get \( x = \frac{2}{4} = 0.5 \).

In a Nutshell

Rational expressions are fractions with polynomials and are simplified and solved much like regular fractions.

Next
Complex Numbers and Their Operations