A rational expression is a fraction where both the numerator and denominator are polynomials.
NoteThe denominatorof a rational expressioncannotbe zero.
Reducing Rational Expressions
Equivalent Rational Expressions
Two rational expressions are equivalent if they have the same value for all values of the variable where they are defined.
NoteEquivalentrational expressionshave the samevaluefor all valuesof the variablewhere they are defined.
Simplifying Rational Expressions
To simplify a rational expression, we need to:
- Factor the numerator and denominator.
- Cancel the common factors.
Cancelingcan only be done with factors, not with terms.
NoteWhen subtractingrational expressions, be carefulto distributethe negativesignto the numeratorof the secondexpression.
Self review1. Simplify the rational expression \$\frac{x^2 - 9}{x^2 - 3x}\$. 2. Multiply the rational expressions \$\frac{x^2 - 4}{x^2 - 2x}\$ and \$\frac{x + 1}{x - 1}\$. 3. Divide the rational expressions \$\frac{x^2 - 4}{x^2 - 2x}\$ by \$\frac{x + 1}{x - 1}\$. 4. Add the rational expressions \$\frac{x^2 - 4}{x^2 - 2x}\$ and \$\frac{x + 1}{x - 1}\$.
