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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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Radical Expressions

Square Roots; Radical Notation

Principal Square Root – square root of b, denoted , for b > 0, is the positive number a such that a² = b.

Examples:

Simplify.

Multiplying Radical Expressions
For any root n and any nonnegative numbers a and b,

Examples:

Simplify

Dividing Radical Expressions

For any root n and any nonnegative numbers a and b, b≠0,

Examples:
Simplify

Homework: pg. 528 #9,13,17,21,23,25,27,29,33,43,45,47,49,51,53,55,57,59,67,71

Rational Exponents

Recall:

For any integer n > 1, we define to be the nth root of a, or

Examples:
Simplify.

For any integers m and n, n > 1, we define to be

Examples:
Simplify.

Examples:
Simplify.

Homework: pg. 575 #3,9,11,13,15,17,19,33,35,37,39,43,45,53,55,63,65

Simplifying Radical Expressions; Adding and Subtracting Radical Expressions

Simplify.

Examples:
Add or Subtract

Homework: pg. 582 #3,5,7,9,11,13,15,17,19,25,29,35,39,49,55,57,59,61

Multiplication and Division of Radical Expression

Examples:
Multiply.

Rationalizing the Denominator:
Examples:
Rationalize the denominator.

Homework: pg. 592 #5,7,13,15,19,23,25,27,33,35,37,39,41,45,47,49,55,61,65,67,75

Radical Equations

Examples:
Solve.

6. For find all values for x for which f(x) = 9.

Homework: pg. 603 #7,9,11,13,17,19,21,25,27,29,31,33,39

Complex Numbers

Examples:

1. Express in terms of i.

2. Express in terms of i.

3. Express − in terms of i.

Complex Number: a + bi, where a is the real part and bi is the imaginary part.

Examples:
1. Simplify:

a. (3 + 12i) + (-8 + 15i)

b. (14 – 6i) – (3 + 22i)

2. Multiply.

a. (4i)(15i)

c. -6i(7 + 8i)

d. (3 – 2i)(8 + i)

e. (9 – 4i)²

f. (7 + 4i)(7 – 4i)

Examples:
Divide.

Powers of i:

Homework: pg. 613 #7,9,13,19,23,25,33,35,45,47,51,53,651,63,65,69,71,73