Rational expression

Definition

A rational expression is a fraction where both the numerator and the denominator are polynomials. It is defined for all values of the variable except those that make the denominator zero.

5 Must Know Facts For Your Next Test

1. The domain of a rational expression excludes values that make the denominator zero.
2. To simplify a rational expression, factor both the numerator and the denominator, then cancel common factors.
3. Rational expressions can be added or subtracted by finding a common denominator.
4. Multiplying rational expressions involves multiplying numerators together and denominators together.
5. Dividing rational expressions involves multiplying by the reciprocal of the divisor.

Review Questions

• What steps are involved in simplifying a rational expression?
• How do you find the domain of a given rational expression?
• Explain how to add two rational expressions with different denominators.

Related terms

Polynomial: An algebraic expression consisting of variables and coefficients, involving only addition, subtraction, multiplication, and non-negative integer exponents.

Reciprocal: The reciprocal of a number is $\frac{1}{a}$ for any non-zero number $a$. For a fraction $\frac{a}{b}$, its reciprocal is $\frac{b}{a}$.

Least Common Denominator (LCD): The smallest common multiple of the denominators of two or more fractions.