Rational expressions and rational equations

Introduction

An expression that is a ratio of two polynomials is called a rational expression.

That is, a rational expression has the form $\dfrac{p(x)}{q(x)}$, where $p(x)$ and $q(x)$ are polynomials.

$\dfrac{2x^2+11}{4x+8}$ is a rational expression.

An equation that contains one or more ratios of polynomials (with polynomials in the numerator and denominator) is called a rational equation.

$\dfrac{x}{2x+5}+5=\dfrac{4x^2+5}{3x-5}$ is a rational equation.

Rational functions, evaluating them, and the domain of a rational function.

Simplifying rational expressions by factoring and canceling common factors.

Multiplying and dividing rational expressions.

Adding and subtracting rational expressions, including the least common denominator.

Simplifying complex fractions.

Solving rational equations and proportions.

Applying rational equations to boat-and-current (upstream and downstream) problems and shared-work problems.