Multiplying and Simplifying Rational Expressions

A. Rational Expressions and Replacements

* A rational expression is an expression that can be written in the form P/Q ; where P
and Q are polynomials .

Ex. Find the numerical value of when x=3.

* Because rational expressions indicate division , we must be careful to avoid
denominators of zero . When a variable is replaced with a number that produces a
denominator equal to zero, the rational expression is not defined.

Ex. Find all numbers for which the given rational expression is not defined.

*Note* The value of the numerator has no bearing on
whether or not a rational expression is
defined. To determine which numbers make
the rational expression not defined, we set
the denominator equal to 0 and solve .

B. Multiplying by 1

* We multiply rational expressions in the same way that we multiply fraction notation in
arithmetic .

Multiplying Rational Expressions: To multiply rational expressions, multiply
numerators and multiply denominators.

For example,

* Any rational expression with the same numerator and denominator is a symbol for 1.

Ex.

Ex.

Ex.

C. Simplifying Rational Expressions

Ex. Simplify each rational expression. ( by factoring and reducing )

D. Multiplying and Simplifying

Ex. Multiply and simplify.