1. Simplifying Rational Expressions
Section 7.1
Simplifying Rational Expressions

2. Rational Expressions
A rational expression is a polynomial divided by another polynomial. or
Fractional algebraic expression
x  – 5
Restriction
The denominator of a rational expression cannot be zero. Any value of the variable that would make the denominator zero is not allowed. 2

3. Basic Rules of Fractions
For any rational expression and any polynomial a, b, and c (where b  0 and c  0), 3

4. Example
Reduce 4

5. Example Simplify. Factor 5 from the numerator.
Apply the basic rule of fractions. 5

6. Example Simplify. Factor the numerator and denominator.
Apply the basic rule of fractions. 6

7. Example Simplify. Factor x from the numerator. Factor the numerator.
Factor the denominator.
Apply the basic rule of fractions. 7

8. Example Simplify. Factor –2 from the numerator.
Remember that when a negative number is factored from a polynomial, the sign of each term in the polynomial changes.
Apply the basic rule of fractions. 8

9. Example
Simplify.
Factor the numerator and the denominator. 9

10. Example
Simplify.