Rational expression

Definition

A rational expression is a fraction where both the numerator and the denominator are polynomials. The denominator cannot be zero.

5 Must Know Facts For Your Next Test

1. Rational expressions can often be simplified by factoring both the numerator and the denominator and then dividing out common factors.
2. To add or subtract rational expressions, find a common denominator before combining.
3. Multiplying rational expressions involves multiplying the numerators together and the denominators together, followed by simplifying if possible.
4. Dividing rational expressions requires multiplying by the reciprocal of the divisor.
5. Rational expressions can have restrictions on their domain, specifically where the denominator equals zero.

Review Questions

• How do you simplify a rational expression?
• What steps must you take to add two rational expressions together?
• Why must you consider the domain when working with rational expressions?

Related terms

Polynomial:

An algebraic expression consisting of terms with variables raised to whole number exponents and coefficients.

Partial Fraction Decomposition:

A method used to express a rational expression as a sum of simpler fractions.

Reciprocal:

The reciprocal of a number is one divided by that number. For a fraction, it involves swapping its numerator and denominator.