Algebra 3/4

Algebra 3/4 delves into advanced algebraic concepts, including polynomial functions, rational expressions, and complex numbers.

Polynomial FunctionsRational ExpressionsComplex Numbers
Polynomial Division and the Remainder TheoremRoots and Zeros of PolynomialsOperations with Complex Numbers
Modeling Real-Life Situations with PolynomialsRational Functions in Science and EngineeringComplex Numbers in Technology
Breaking Down ProblemsChecking Your Answers
Polynomial FunctionsRational ExpressionsComplex NumbersPolynomial Division ...Roots and Zeros of P...Operations with Comp...Modeling Real-Life S...Rational Functions i...Complex Numbers in T...Breaking Down Proble...Checking Your Answer...
Basic Concepts

Rational Expressions

Understanding Rational Expressions

A rational expression is a fraction where the numerator and denominator are both polynomials. They're like regular fractions, but with algebraic expressions!

Simplifying Rational Expressions

To simplify, factor both the numerator and denominator and cancel out any common factors. Always check for restrictions: values that make the denominator zero are not allowed.

Operations with Rational Expressions

  • Addition/Subtraction: Get a common denominator, just like with regular fractions.
  • Multiplication/Division: Multiply numerators and denominators straight across; for division, multiply by the reciprocal.

When Do We Use Rational Expressions?

Rational expressions appear in science, engineering, and even finance when dealing with rates, ratios, and proportions.

Examples

  • \( \frac{x^2 - 9}{x + 3} \) simplifies to \( x - 3 \) for \( x eq -3 \).

  • Adding \( \frac{1}{x} + \frac{2}{x^2} \) gives \( \frac{x + 2}{x^2} \).

In a Nutshell

Rational expressions are fractions made up of polynomials.

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Complex Numbers