A rational expression is a fraction where both the numerator and denominator are polynomials.
The denominatorof a rational expressioncannotbe zero.
Simplifying Rational Expressions
A rational expression is in its simplest form when the numerator and denominator have no common factors other than 1.
To simplify a rational expression:
- Factor the numerator and denominator completely.
- Cancel out any common factors.
Do not cancel terms that are addedor subtracted. Only factorscan be cancelled.
Multiplying and Dividing Rational Expressions
Multiplying Rational Expressions
To multiply two rational expressions:
- Multiply the numerators together.
- Multiply the denominators together.
- Simplify the result by factoring and cancelling any common factors.
Be careful with subtraction. Remember to distributethe negative signacross the numeratorof the second expression.
Applications of Rational Expressions
Rational expressions are used to model and solve problems in various fields, such as:
- Physics: Calculating resistance in parallel circuits.
- Economics: Modelling supply and demand curves.
- Biology: Describing population growth with limited resources.
1. Simplify the rational expression \$\frac{x^2 - 9}{x^2 - 6x + 9}\$. 2. Multiply \$\frac{x + 1}{x^2 - 4}\$ by \$\frac{x - 2}{x + 3}\$. 3. Divide \$\frac{x^2 - 1}{x + 2}\$ by \$\frac{x - 1}{x^2 - 4}\$. 4. Add \$\frac{1}{x^2 - 4}\$ and \$\frac{1}{x^2 - x}\$.
How do rational expressionshelp us model real-worldsituations? What are the limitationsof these models?
