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Rational Expressions and Their Simplification
Radical Expressions and Equations
Algebraic Expressions
Simplifying Algebraic Expressions
Rational Expressions and Functio
Rational Expressions and Functions
Radical Expressions
Rational Expressions Worksheet
Adding and Subtracting Rational Expressions
Rational Expressions
Multiplying and Dividing Rational Expressions
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 & Functions

Objective: To define and simplify rational
expressions, describe their domains, and
multiply and divide rational expressions.

Definition 1

Rational expression – an algebraic
__________ with a variable

Examples

Remember: Denominator cannot equal zero!

Definition 2

rational function – a __________ of two
polynomials

where p(x) and q(x) are polynomials and
where q(x) is not zero.

Find all numbers in the domain of each
rational function. Write using interval
notation.

Find all numbers in the domain of each
rational function. Write using interval
notation.

Fundamental Property
of Rational Numbers

See bottom of page 415.

Simplifying a Rational Expression

1. ______ numerator and denominator.
2. Apply the fundamental property.
(__________ common factors.)
3. __________.
4. Note exclusions. (values that make
denominator equal zero)

Watch & think.
Simplify. Note exclusions.

EXAMPLES – Simplify.

Opposite Factors

After factoring, if you have “__________
factors”, you can factor out –1 and then
cancel.

For example: (x - 3) & (3 - x) are
opposites.
- (3 - x) =(-3 + x)= (x – 3)

Simplify.

Multiplying and Dividing
Rational Expressions

Page 418

Review of Multiplying Fractions

Rule: top x top
bottom x bottom

Want to Cancel before Multiplying? Fine!
(It’s like reducing first!) But…
Cancel only top to bottom!

Multiplying Rational Expressions

1. __________, if possible.
2. Cancel out common __________ on top &
bottom.
3. Multiply remaining factors.
4. Simplify, if needed.

Multiplication Examples

Dividing Algebraic Fractions

Reminder: When dividing fractions,
multiply by the __________. (Flip the
second fraction and multiply.)

Steps for Dividing
Rational Expressions

1. Flip second fraction and change division sign
to multiplication sign.
2. Follow same steps as with multiplication.

Division Examples

IMPORTANT REMINDER!!!!

You can only cancel a monomial with a
monomial, or a binomial with a binomial, etc.
You CANNOT cancel part of a polynomial
with a monomial!!!
You MUST __________ before canceling!!

SUMMARY

Factor, cancel, multiply.
If dividing, multiply by reciprocal of 2nd
fraction.