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Rational Expressions and Their Simplification
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Adding and Subtracting Rational Expressions
Rational Expressions
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Dividing Fractions, Mixed Numbers, and Rational Expressions
Multiplying and Dividing Rational Expressions
Multiplying and Dividing Rational Expressions
Simplifying Rational Expressions
Complex Rational Expressions
Rational Expressions and Equations
Integration of Polynomial Rational Expressions
Algebraic Expressions
Radical Expressions & Radical Functions
Rational Class and Expression Evaluator
Adding and Subtracting Rational Expressions
Rational Expressions
Radical Expressions
Multiplying Rational Expressions
Rational Expressions and Common Denominators
rational expressions
Polynomial Expressions
Rational Functions, and Multiplying and Dividing Rational Expressions
Simplifying Radical Expressions
Adding and Subtracting Rational Expressions
Rational Expressions and Equations
Rational Expressions
RATIONAL EXPRESSIONS II
Simplifying Expressions
Quadratic Expressions,Equations and Functions
RATIONAL EXPRESSIONS
Absolute Value and Radical Expressions,Equations and Functions
Rational Expressions & Functions

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Rational Expressions and Functions: Multiplying and Dividing

Rational Expressions

Rational Functions

Simplifying Rational Expressions

1.Write the numerator and denominator in factored form.
2.Divide out all common factors in the numerator and denominator.
3.Multiply the remaining factors in the numerator and the
remaining factors in the denominator.

FYI

The binomial a –b is the opposite of the binomial b –a.
Algebraically, write a –b as–(b –a) or –1(b –a).

Example 1

Find the function values indicated, provided the value exists.
State the domain of the function.
 

f(0) r(2)
f(-1) r(-3)
Domain: Domain:
Rule for Multiplying Rational Expressions

, where A, B, C, and D are polynomials where B, D ≠ 0.

Example 2
Multiply. Do not simplify. Assume that all denominators are nonzero.



Example 3
Simplify by removing a factor equal to 1.


Example 4
Write in simplified form. List all restrictions on the domain.
 
Restrictions: Restrictions: Restrictions:
Example 5
Multiply and, if possible, simplify.

Rule for Dividing Rational Expressions

where A, B, C, and D are polynomials where B, C, D ≠0.

Example 6
Divide and, if possible, simplify.

Example 7
Divide and, if possible, simplify.

Example 8
Write in simplified form. List all restrictions on the domain.
 
Restrictions: Restrictions:
Example 9
Perform the indicated operations and, if possible, simplify.

Example 10
Find and explain the mistake.