Advanced algebraic concepts including polynomials, rational expressions, and complex numbers.
Rational expressions are fractions with polynomials in the numerator and denominator. You can simplify, multiply, divide, add, or subtract them—just like with numerical fractions!
Factor both the numerator and denominator and cancel any common factors. Always check for restrictions—values that would make the denominator zero.
To solve equations with rational expressions, find a common denominator, multiply both sides to eliminate denominators, then solve the resulting equation.
Rational expressions are used in everything from calculating speed to understanding rates in chemistry.
Rational equations can describe things like mixing solutions, comparing speeds, or sharing resources.
Simplifying \( \frac{x^2 - 4}{x^2 - 2x} = \frac{(x + 2)(x - 2)}{x(x - 2)} = \frac{x + 2}{x} \) (as long as \( x eq 0, 2 \))
Solving \( \frac{1}{x} + \frac{1}{2} = 1 \) gives \( x = 2 \ )
Rational expressions are fractions made from polynomials, and can be simplified or solved like regular fractions.