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Arithmetic Operations with Numerical Fractions
Multiplying a Polynomial by a Monomial
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Simplifying Fractions 3
Factoring quadratics
Special Products
Writing Fractions as Percents
Using Patterns to Multiply Two Binomials
Adding and Subtracting Fractions
Solving Linear Inequalities
Adding Fractions
Solving Systems of Equations -
Exponential Functions
Integer Exponents
Example 6
Dividing Monomials
Multiplication can Increase or Decrease a Number
Graphing Horizontal Lines
Simplification of Expressions Containing only Monomials
Decimal Numbers
Negative Numbers
Subtracting Polynomials
Adding and Subtracting Fractions
Powers of i
Multiplying and Dividing Fractions
Simplifying Complex Fractions
Finding the Coordinates of a Point
Fractions and Decimals
Rational Expressions
Solving Equations by Factoring
Slope of a Line
Percent Introduced
Reducing Rational Expressions to Lowest Terms
The Hyperbola
Standard Form for the Equation of a Line
Multiplication by 75
Solving Quadratic Equations Using the Quadratic Formula
Raising a Product to a Power
Solving Equations with Log Terms on Each Side
Monomial Factors
Solving Inequalities with Fractions and Parentheses
Division Property of Square and Cube Roots
Multiplying Two Numbers Close to but less than 100
Solving Absolute Value Inequalities
Equations of Circles
Percents and Decimals
Integral Exponents
Linear Equations - Positive and Negative Slopes
Multiplying Radicals
Factoring Special Quadratic Polynomials
Simplifying Rational Expressions
Adding and Subtracting Unlike Fractions
Graphuing Linear Inequalities
Linear Functions
Solving Quadratic Equations by Using the Quadratic Formula
Adding and Subtracting Polynomials
Adding and Subtracting Functions
Basic Algebraic Operations and Simplification
Simplifying Complex Fractions
Axis of Symmetry and Vertices
Factoring Polynomials with Four Terms
Evaluation of Simple Formulas
Graphing Systems of Equations
Scientific Notation
Lines and Equations
Horizontal and Vertical Lines
Solving Equations by Factoring
Solving Systems of Linear Inequalities
Adding and Subtracting Rational Expressions with Different Denominators
Adding and Subtracting Fractions
Solving Linear Equations
Simple Trinomials as Products of Binomials
Solving Nonlinear Equations by Factoring
Solving System of Equations
Exponential Functions
Computing the Area of Circles
The Standard Form of a Quadratic Equation
The Discriminant
Dividing Monomials Using the Quotient Rule
Squaring a Difference
Changing the Sign of an Exponent
Adding Fractions
Powers of Radical Expressions
Steps for Solving Linear Equations
Quadratic Expressions Complete Squares
Fractions 1
Properties of Negative Exponents
Factoring Perfect Square Trinomials
Solving Quadratic Equations Using the Square Root Property
Dividing Rational Expressions
Quadratic Equations with Imaginary Solutions
Factoring Trinomials Using Patterns
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Simplifying Rational Expressions

1. need to identify any restrictions on the value of the variables

a. IE what will make the denominator zero

i. 2xy = 0 .: x = 0, y = 0. .: x,y cannot equal zero are the restrictions

2. Now reduce the expression into simplest terms.

a. Look at factoring the numerator or the denominator first, then use exponent laws or cancelling like terms.

i. The value of x can be reduced

Factoring the numerator and/or denominator

1. Restrictions , x cannot equal +/- 3.

a. Via inspection or factoring (x-3)(x+3)

2. the expression reduces to 5(x -3)/(x-3)(x+3), which simplifies to 5/(x+3)

3. Note when graphing the function there is no change to the output of the function. The graph is the same using the un-simplified form or the reduced form. The reduced form is easier to work with while doing the graphing by hand

Complex Factoring of a rational expression

1. Restrictions on the denominator m cannot equal 0, -1/2, 4/3.

a. Factor the denominator m(6m 2 -5m-4) m(m+.5)(m-1.33)

2. Nothing can be factored further as there is nothing in common on top and bottom

1. Factor the numerator and denominator (if possible)

a. Simply

b. Complex

c. Multiple factoring

2. State restrictions of the denominator a. the restrictions are any value that will make the denominator equal zero

3. Cancel any terms which are multiplied on top and bottom.

4. Write out the final terms and state any restrictions.

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