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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.