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TUTORIALS:

Absolute Values
Solving Two-Step Equations Algebraically
Multiplying Monomials
Factoring Trinomials
Solving Quadratic Equations
Power Functions and Transformations
Composition of Functions
Rational Inequalities
Equations of Lines
Graphing Logarithmic Functions
Elimination Using Multiplication
Multiplying Large Numbers
Multiplying by 11
Graphing Absolute Value Inequalities
Polynomials
The Discriminant
Reducing Numerical Fractions to Simplest Form
Addition of Algebraic Fractions
Graphing Inequalities in Two Variables
Adding and Subtracting Rational Expressions with Unlike Denominators
Multiplying Binomials
Graphing Linear Inequalities
Properties of Numbers and Definitions
Factoring Trinomials
Relatively Prime Numbers
Point
Inequalities
Rotating a Hyperbola
Writing Algebraic Expressions
Quadratic and Power Inequalities
Solving Quadratic Equations by Completing the Square
BEDMAS & Fractions
Solving Absolute Value Equations
Writing Linear Equations in Slope-Intercept Form
Adding and Subtracting Rational Expressions with Different Denominators
Reducing Rational Expressions
Solving Absolute Value Equations
Equations of a Line - Slope-intercept form
Adding and Subtracting Rational Expressions with Unlike Denominators
Solving Equations with a Fractional Exponent
Simple Trinomials as Products of Binomials
Equivalent Fractions
Multiplying Polynomials
Slope
Graphing Equations in Three Variables
Properties of Exponents
Graphing Linear Inequalities
Solving Cubic Equations by Factoring
Adding and Subtracting Fractions
Multiplying Whole Numbers
Straight Lines
Solving Absolute Value Equations
Solving Nonlinear Equations
Factoring Polynomials by Finding the Greatest Common Factor
Logarithms
Algebraic Expressions Containing Radicals 1
Addition Property of Equality
Three special types of lines
Quadratic Inequalities That Cannot Be Factored
Adding and Subtracting Fractions
Coordinate System
Solving Equations
Factoring Polynomials
Solving Quadratic Equations
Multiplying Radical Expressions
Solving Quadratic Equations Using the Square Root Property
The Slope of a Line
Square Roots
Adding Polynomials
Arithmetic with Positive and Negative Numbers
Solving Equations
Powers and Roots of Complex Numbers
Adding, Subtracting and Finding Least Common Denominators
What the Factored Form of a Quadratic can tell you about the graph
Plotting a Point
Solving Equations with Variables on Each Side
Finding the GCF of a Set of Monomials
Completing the Square
Solving Equations with Radicals and Exponents
Solving Systems of Equations By Substitution
Adding and Subtracting Rational Expressions
Percents
Laws of Exponents and Dividing Monomials
Factoring Special Quadratic Polynomials
Radicals
Solving Quadratic Equations by Completing the Square
Reducing Numerical Fractions to Simplest Form
Factoring Trinomials
Writing Decimals as Fractions
Using the Rules of Exponents
Evaluating the Quadratic Formula
Rationalizing the Denominator
Multiplication by 429
Writing Linear Equations in Point-Slope Form
Multiplying Radicals
Dividing Polynomials by Monomials
Factoring Trinomials
Introduction to Fractions
Square Roots
   
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Adding, Subtracting, and Finding Least Common Denominators

Recall: When you add or subtract fractions with like denominators, you combine the tops and leave the bottoms alone. Of course, you reduce to lowest terms when you’re done.

Examples:

New Stuff:

  • Adding rational expressions with like denominators

Procedure: (Adding Rational Expressions with Like Denominators)

Add the tops and leave the bottoms alone:

Example:

Add

  • Subtracting rational expressions with like denominators

Procedure: (Subtracting Rational Expressions with Like Denominators)

Subtract the tops and leave the bottoms alone:

Example:

NOTE THE USE OF PARENTHESES IN THE WORK FOR THIS EXAMPLE!!

  • Least common multiples and least common denominators.

Recall:

  • The least common multiple of a collection of numbers is the smallest number that each of the given numbers is a factor of.

Example:

Find the least common multiple of 9, 12, and 15.

  • The least common denominator of a collection of fractions is the least common multiple of the denominators.

Example:

Find a least common denominator for

New Stuff:

  • The least common multiple (LCM) of a polynomial and least common denominator (LCD) of a rational expression share the same relationship.

Procedure: (Finding the LCD of a collection of rational expressions)

1. Factor each denominator completely.

2. Build the LCM of the denominators as follows:

  • Write down the factorization of the first denominator.
  • Look at the second denominator and compare it to what you have just written. Write down each factor of the second denominator that does NOT appear in the factorization of the first. (If a factor is the same, but appears more times in the second denominator than in the first, then add as many copies of that factor as are necessary.)
  • Look at the third denominator (if there is one). Compare it to what you have written so far. Write down each factor of the third denominator that does not yet appear in the written list of factors.
  • Repeat the last step for every remaining denominator, until all have been accounted for.
  • When you are done, the LCM should contain each factor the greatest number of times that it occurs in any one denominator.

3. The LCD is the LCM of the denominators.

4. “Fix” the rational expressions by multiplying the top and bottom of each by any factors of the LCD which do not appear in the original denominator.

 

Example:

Find equivalent expressions which have the LCD for each of the following collections of rational expressions.

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