# Multiplying and Simplifying Rational Expressions

# 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.

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