- Multiplication Of Rational Expressions
- Division Of Rational Expressions

Inside Collection (Textbook): Elementary Algebra

Summary:

This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.

A detailed study of arithmetic operations with rational expressions is presented in this chapter, beginning with the definition of a rational expression and then proceeding immediately to a discussion of the domain. The process of reducing a rational expression and illustrations of multiplying, dividing, adding, and subtracting rational expressions are also included. Since the operations of addition and subtraction can cause the most difficulty, they are given particular attention. We have tried to make the written explanation of the examples clearer by using a "freeze frame" approach, which walks the student through the operation step by step.

The five-step method of solving applied problems is included in this chapter to show the problem-solving approach to number problems, work problems, and geometry problems. The chapter also illustrates simplification of complex rational expressions, using the combine-divide method and the LCD-multiply-divide method.

Objectives of this module: be able to multiply and divide rational expressions.

- Multiplication Of Rational Expressions
- Division Of Rational Expressions

Rational expressions are multiplied together in much the same way that arithmetic fractions are multiplied together. To multiply rational numbers, we do the following:

- Definition 1: Method for Multiplying Rational Numbers
- Reduce each fraction to lowest terms.
- Multiply the numerators together.
- Multiply the denominators together.

Rational expressions are multiplied together using exactly the same three steps. Since rational expressions tend to be longer than arithmetic fractions, we can simplify the multiplication process by adding one more step.

- Definition 2: Method for Multiplying Rational Expressions
- Factor all numerators and denominators.
- Reduce to lowest terms first by dividing out all common factors. (It is perfectly legitimate to cancel the numerator of one fraction with the denominator of another.)
- Multiply numerators together.
- Multiply denominators. It is often convenient, but not necessary, to leave denominators in factored form.

Perform the following multiplications.

Perform each multiplication.

To divide one rational expression by another, we first invert the divisor then multiply the two expressions. Symbolically, if we let

Perform the following divisions.

Perform each division.

For the following problems, perform the multiplications and divisions.

1

1

*((Reference))* If

.

*((Reference))* Classify the polynomial

binomial; 2; 4, 2

*((Reference))* Find the product:

*((Reference))* Translate the sentence “four less than twice some number is two more than the number” into an equation.

*((Reference))* Reduce the fraction

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Comments:"Reviewer's Comments: 'I recommend this book for courses in elementary algebra. The chapters are fairly clear and comprehensible, making them quite readable. The authors do a particularly nice job […]"