Factor out GCF Count number of terms Factor by Grouping Check for: Difference of perfect squares Sum of perfect cubes Difference of perfect cubes 1.Check for perfect square trinomial 2.Use big X factoring Check each factor to see if it can be factored further

Section P.6

 How do we simplify, add, subtract, multiply, and divide rational expressions?

 A rational expression is a quotient (division) of two polynomials.  The domain of an expression is the set of all real numbers for which the expression is defined. ◦ The x’s that work  Domain restrictions are numbers that are not part of the domain. ◦ The x’s that don’t work (division by zero)

Find the domain restrictions of each rational expression. a) x ≠ 2 b) x ≠ ±1

1. Factor the numerator and denominator completely. 2. Cancel common factors.

 Simplify and state the domain restrictions:

1. Factor everything completely. 2. Cancel common factors. 3. Write the remaining factors in one fraction.

 Simplify and state the domain restrictions:

1. Invert the divisor ◦ Flip the second fraction 2. Multiply

 Simplify and state the domain restrictions:

 Read Section P.6  Page 67 #1-53 Odd, 70  You have 15 minutes to work, then more notes.

 Find all numbers that must be excluded from the domain of each rational expression.  Simplify each rational expression. Find all numbers that must be excluded from the domain of each rational expression.

 Simplify and state the domain restrictions

1. Find a common denominator 2. Convert all expressions to the common denominator 3. Add/subtract numerators  If subtracting, remember to distribute the “–” 4. Place the result above the common denominator 5. Simplify if possible

 Simplify and state the domain restrictions:

1. Factor each denominator. 2. List all factors of all denominators. ◦ If a factor is repeated in one denominator, it must be repeated in the LCD. 3. The product of the listed factors is the LCD.

 Simplify and state the domain restrictions:

 Read Section P.6  Page 67 #1-53 Odd, 70  You have the rest of class to work on the assignment.

 In Exercises 25-44, add or subtract as indicated.

 Simplify and state the domain restrictions:

 Complex Rational Expressions, also called complex fractions, are a fraction of fractions  Simplified by: 1.Simplify the top half 2.Simplify the bottom half 3.Divide the two resulting fractions (flip 2 nd and multiply)

 Read Section P.6  Page 67 #1-53 Odd, 70

 P.1-P.4 Quizzes are graded  New seating chart next week – Mr. Szwast by end of Wednesday if you need to sit in front to see the board  Tutoring ◦ Lunch in 454 ◦ After school in 410

 Simplify each complex rational expression.