Algebra Tutorials!  
Monday 15th of July
Rotating a Parabola
Multiplying Fractions
Finding Factors
Miscellaneous Equations
Mixed Numbers and Improper Fractions
Systems of Equations in Two Variables
Literal Numbers
Adding and Subtracting Polynomials
Subtracting Integers
Simplifying Complex Fractions
Decimals and Fractions
Multiplying Integers
Logarithmic Functions
Multiplying Monomials
The Square of a Binomial
Factoring Trinomials
The Pythagorean Theorem
Solving Radical Equations in One Variable
Multiplying Binomials Using the FOIL Method
Imaginary Numbers
Solving Quadratic Equations Using the Quadratic Formula
Solving Quadratic Equations
Order of Operations
Dividing Complex Numbers
The Appearance of a Polynomial Equation
Standard Form of a Line
Positive Integral Divisors
Dividing Fractions
Solving Linear Systems of Equations by Elimination
Multiplying and Dividing Square Roots
Functions and Graphs
Dividing Polynomials
Solving Rational Equations
Use of Parentheses or Brackets (The Distributive Law)
Multiplying and Dividing by Monomials
Solving Quadratic Equations by Graphing
Multiplying Decimals
Use of Parentheses or Brackets (The Distributive Law)
Simplifying Complex Fractions 1
Adding Fractions
Simplifying Complex Fractions
Solutions to Linear Equations in Two Variables
Quadratic Expressions Completing Squares
Dividing Radical Expressions
Rise and Run
Graphing Exponential Functions
Multiplying by a Monomial
The Cartesian Coordinate System
Writing the Terms of a Polynomial in Descending Order
Quadratic Expressions
Solving Inequalities
Solving Rational Inequalities with a Sign Graph
Solving Linear Equations
Solving an Equation with Two Radical Terms
Simplifying Rational Expressions
Intercepts of a Line
Completing the Square
Order of Operations
Factoring Trinomials
Solving Linear Equations
Solving Multi-Step Inequalities
Solving Quadratic Equations Graphically and Algebraically
Collecting Like Terms
Solving Equations with Radicals and Exponents
Percent of Change
Powers of ten (Scientific Notation)
Comparing Integers on a Number Line
Solving Systems of Equations Using Substitution
Factoring Out the Greatest Common Factor
Families of Functions
Monomial Factors
Multiplying and Dividing Complex Numbers
Properties of Exponents
Multiplying Square Roots
Adding or Subtracting Rational Expressions with Different Denominators
Expressions with Variables as Exponents
The Quadratic Formula
Writing a Quadratic with Given Solutions
Simplifying Square Roots
Adding and Subtracting Square Roots
Adding and Subtracting Rational Expressions
Combining Like Radical Terms
Solving Systems of Equations Using Substitution
Dividing Polynomials
Graphing Functions
Product of a Sum and a Difference
Solving First Degree Inequalities
Solving Equations with Radicals and Exponents
Roots and Powers
Multiplying Numbers
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Adding and Subtracting Rational Expressions 

1. To add rational expressions you must have common denominators, then you add the numerators. [The result must be checked to see if it will reduce to simpler form.]



2. Factor and simplify:

2. If the rational expressions do not have common denominators you must factor the denominators and find the least common denominator (LCD).

Raise all fractions, so that they have common denominators, then add the numerators.

NOTE: With different denominators find the LCD and add using one of two methods: (1) raise each with LCD or (2) write LCD and find missing factor for each numerator.


(2) Write the LCD then start with the first numerator – compare its denominator with the LCD and multiply by its missing factor. Write the next sign and next numerator – compare its denominator and multiply by its missing factor.


Definitions and Notes

If necessary, factor the denominators of the examples in order to find the LCD. Leave the denominator of the results in factored form. [Always check and/or factor the numerator of the results in order to reduce the answer to simplest form.]

Method (1): Raise each fraction to have LCD = (x + 3)(x – 3)(x – 2)

[Do not cancel.] Remove parentheses and combine numerators. [Watch negative signs.]

To subtract add the opposite or Negate second numerator: (-1)(2)(x+3) = –2x – 6.

Method (2): Compare each factored denominator with LCD = (x + 3)(x – 3)(x – 2)

and find “missing factors”.

[NOTE: “mf” means “missing factor” ]

Remove parentheses and collect terms: [Watch negative signs.]

[Leave in factored form.]

Check: Let x = 5 (unique prime) in the given example and in the answer:

Always check results by either method to see if the rational expression can be reduced.

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