Rationele uitdrukkingen

In a growing city, expanding limits and new housing developments increase the population, leading to crowding. Population density quantifies how crowded the city becomes.

It can be modeled as a rational expression in terms of time, t, a fraction where the numerator is the total population and the denominator is the total area.

The domain of this rational expression is found by factoring the denominator and excluding values that make it zero.

This can be visualized on a graph as breaks where the function becomes undefined.

Simplifying a rational expression involves factoring the numerator and the denominator and canceling common factors—only when the denominator is not zero.

Multiplying rational expressions involves factoring each expression into its simplest form, and then multiplying the numerators and the denominators together. The resulting expression is simplified by canceling any common factors.

Adding these expressions requires a common denominator, formed by multiplying the denominators and including shared terms only once. Each expression is rewritten with this base and a numerator adjusted with the extra terms. Once the denominators are aligned, the numerators are combined to obtain the result.