# Essay on Rational Algebraic Expressions

4. Rational Algebraic Expressions

Note You need to understand how to multiply algebraic expressions using the distributive law before starting work on this tutorial. If you feel you need to review this, go back to 3. Multiplying and Factoring Algebraic Expressions.

Q What is a Rational Expression?

Rational Expression

A rational expression is an algebraic expression of the form P/Q, where P and Q are simpler expressions (usually polynomials), and the denominator Q is not zero.

A rational number is any number that can be written in the form a/b, where a and b are integers and b ≠ 0. it is necessary to exclude 0 because the fraction represents a ÷ b, and division by zero is undefined.

A

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This process (cancelling first, then multiplying) works with rational expressions, too. * Simplify the following expression:

Simplify by cancelling off duplicate factors:

(If you're not sure how the variable parts were simplified above, you may want to review how to simplify expressions with exponents.)

Then the answer is:

DIVISION

Dividing Rational Expressions (page 2 of 2)

For dividing rational expressions, you will use the same method as you used for dividing numerical fractions: when dividing by a fraction, you flip-n-multiply. For instance: * Perform the indicated operation:

To simplify this division, I'll convert it to multiplication by flipping what I'm dividing by; that is, I'll switch from dividing by a fraction to multiplying by that fraction's reciprocal. Then I'll simplify as usual:

Can the 2's cancel off from the 20's? No! This is as simplified as the fraction gets.

Division works the same way with rational expressions. * Perform the indicated operation:

To simplify this, first I'll flip-n-multiply. Then, to simplify the multiplication, I'll factor the numerators and denominators, and then cancel any duplicated factors. My work looks like this:

Then the answer is: Copyright © Elizabeth Stapel 2003-2011 All Rights Reserved

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