Simplifying Rational Expressions Section 7.1 Simplifying Rational Expressions

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

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

Example Reduce 4

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

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

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

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

Example Simplify. Factor the numerator and the denominator. 9

Example Simplify.