Multiplication of Rational expressions is in some ways ...



Chapter 11 – Rational Functions

Lesson #5 – Multiplying and Dividing Rational Expressions

OBJECTIVES:

- Perform operations with rational expressions in a real-world example.

- Learn how to multiply and divide rational expressions.

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Multiplication and division of Rational expressions is in some ways EASIER than addition and subtraction of rational expressions (previous lesson) because a common denominator does not have to be found.

A lot of times in math students have to use past concepts to be able to work all the way through the new problems.  In this section students will have to remember how to factor, simplify rational expressions and multiply polynomials to be able to complete the multiplication or division problems.

Multiplying Rational Expressions

[pic]

Q and S do not equal 0.

Step 1: Factor both the numerator and the denominator.

Step 2: Write as one fraction.

Step 3: Simplify the rational expression.

Step 4: Multiply any remaining factors in the numerator and/or denominator.

Show an example using multiplication and go through step by step to make sure the students understand the process.

Example One: Multiply [pic]

Step 1: Factor both the numerator and the denominator.

Since our problem’s denominators are already factored, we can move on.

Step 2: Write as one fraction.

[pic]

Step 3: Simplify the rational expression.

[pic] *Exclude values of original data making denom. = 0.

There are no remaining factors in the numerator or denominator so we are done.

Example Two: Multiply [pic]

Step 1: Factor both the numerator and the denominator.

AND

Step 2: Write as one fraction.

[pic] *Factor the num. and denom.

Step 3: Simplify the rational expression.

AND

Step 4: Multiply any remaining factors in the numerator and/or denominator.

[pic]

[pic] *Divide out 2,(x+2), and (x-3).

[pic] *Exclude values making denom. zero.

Dividing Rational Expressions

[pic]

where Q, S, and R do not equal 0.

Step 1: Write as multiplication of the reciprocal.

Step 2: Multiply the rational expressions as shown above.

Example Three: Divide [pic]

Step 1: Write as multiplication of the reciprocal.

AND

Step 2: Multiply the rational expressions as shown above.

[pic]=

[pic] *Multiply by the reciprocal.

[pic] *Simplify by dividing out common factors.

[pic] *Multiply denom. and num. out.

[pic] *Exclude values making denom. zero.

Example Four: Divide [pic]

Step 1: Write as multiplication of the reciprocal.

AND

Step 2: Multiply the rational expressions as shown above.

[pic] *Multiply by the reciprocal

[pic] *Simplify out by dividing common factors.

[pic] *Exclude values to prove denom. is zero.

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Homework: Pg. 550/#28, 34, 37, 49

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