Section 1-4
1
Math 150 Lecture Notes
Rational Expressions
A fractional expression is the quotient of two algebraic expressions.
A rational expression is a fractional expression in which both numerator and denominator are
polynomials.
The Domain of an Algebraic Expression
The domain of an algebraic expression is the set of real numbers for which the variable is
defined.
Simplifying Rational Expressions
To simplify a rational expression, factor both numerator and denominator and divide both by any
common factors.
Multiplying/Dividing Rational Expressions
To multiply rational expressions, use the definition of multiplication of fractions (multiply
numerators for the new numerator and multiply denominators for the new denominator).
Note: In actual practice, factor each numerator and denominator first. Write as a new fraction
with the product of factors in the numerator and denominator. Simplify before actually
multiplying the numerators and denominators.
Adding/Subtracting Rational Expressions
To add or subtract all types of expressions, they must be like terms. For rational expressions,
that includes a common denominator.
