Algebra 11-3 and 11-4. Simplifying Rational Expressions A rational expression is an algebraic fraction whose numerator and denominator are polynomials.

Slides:



Advertisements
Similar presentations
EXAMPLE 3 Standardized Test Practice SOLUTION 8x 3 y 2x y 2 7x4y37x4y3 4y4y 56x 7 y 4 8xy 3 = Multiply numerators and denominators. 8 7 x x 6 y 3 y 8 x.
Advertisements

Warm Up Simplify each expression. Factor the expression.
11.3 – Rational Functions. Rational functions – Rational functions – algebraic fraction.
Pre-Calculus Notes §3.7 Rational Functions. Excluded Number: A number that must be excluded from the domain of a function because it makes the denominator.
MTH 092 Section 12.1 Simplifying Rational Expressions Section 12.2
Multiplying & Dividing Rational Expressions. Simplified form of a rational expression - Means the numerator and denominator have NO common factors. To.
Lesson 8-1: Multiplying and Dividing Rational Expressions
Rational Expressions Simplifying Algebra B.
Rational Expressions rational expression: quotient of two polynomials x2 + 3x x + 2 means (x2 + 3x - 10) ÷ (3x + 2) restrictions: *the denominator.
Simplify Rational Algebraic Expressions In the previous section on polynomials, we divided a polynomial by a binomial using long division. In this section,
COLLEGE ALGEBRA P.5 – Rational Expressions P.6 – Complex Numbers.
Section P6 Rational Expressions
Simplify Rational Expressions
8.4: Do Now: Multiply the expression. Simplify the result.
Warm-Up Simplify.. CA STANDARDS 12.0: Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing to.
Notes Over 9.4 Simplifying a Rational Expression Simplify the expression if possible. Rational Expression A fraction whose numerator and denominator are.
Chapter 9: Rational Expressions Section 9-1: Multiplying and Dividing Rationals 1.A Rational Expression is a ratio of two polynomial expressions. (fraction)
Section 8.2: Multiplying and Dividing Rational Expressions.
Section 9-3a Multiplying and Dividing Rational Expressions.
Vocabulary  Rational Expression – a ratio of 2 polynomial expressions.  Operations with rational numbers and rational expressions are similar.  Just.
 Multiply rational expressions.  Use the same properties to multiply and divide rational expressions as you would with numerical fractions.
Operations on Rational Expressions. Rational expressions are fractions in which the numerator and denominator are polynomials and the denominator does.
Warm-up Factor each polynomial. 1. 4x 2 – 6x2. 15y y 3. n 2 + 4n p 2 – p – 42.
§ 7.2 Multiplying and Dividing Rational Expressions.
Bell Ringer 9/18/15 1. Simplify 3x 6x 2. Multiply 1 X Divide 2 ÷
11.4 Multiply and Divide Rational Expressions. SIMPLIFYING RATIONAL EXPRESSIONS Step 1: Factor numerator and denominator “when in doubt, write it out!!”
8 4 Multiply & Divide Rational Expressions
Multiplying and Dividing Rational Expressions
8.4 Multiply and Divide Rational Expressions
Bell Ringer 2/9/15 1. Simplify 3x 6x 2. Multiply 1 X Divide 2 ÷ Add Subtract 2 _
§ 7.7 Simplifying Complex Fractions. Martin-Gay, Beginning and Intermediate Algebra, 4ed 22 Complex Rational Expressions Complex rational expressions.
Rational Expressions Simplifying. Polynomial – The sum or difference of monomials. Rational expression – A fraction whose numerator and denominator are.
To simplify a rational expression, divide the numerator and the denominator by a common factor. You are done when you can no longer divide them by a common.
9.4 Rational Expressions (Day 1). A rational expression is in _______ form when its numerator and denominator are polynomials that have no common factors.
Section 6.2 Multiplication and Division. Multiplying Rational Expressions 1) Multiply their numerators and denominators (Do not FOIL or multiply out the.
Welcome to Algebra 2 Rational Equations: What do fractions have to do with it?
3.9 Mult/Divide Rational Expressions Example 1 Multiply rational expressions involving polynomials Find the product. Multiply numerators and denominators.
Warm-Up Exercises Perform the operation. 1. x x + 36 x 2 – x5x x 2 – 6x + 9 · x 2 + 4x – 21 x 2 + 7x ANSWERS x + 3 x – 12 ANSWERS 5 x – 3.
Operations on Rational Expressions MULTIPLY/DIVIDE/SIMPLIFY.
Multiplying and Dividing Rational Expressions
Do Now: Multiply the expression. Simplify the result.
Simplifying Rational Expressions
Multiplying and Dividing Fractions
Section P6 Rational Expressions
8.1 Multiplying and Dividing Rational Expressions
Rational expressions 8.11.
Multiplying and Dividing Rational Expressions
8.4 Multiply & Divide Rational Expressions
Notes Over 11.4 Simplifying a Rational Expression
Without a calculator, simplify the expressions:
Section 8-2: Multiplying and Dividing Rational Expressions
Look for common factors.
Mult/Divide Rational Expressions
Simplify Complex Rational Expressions
Warm-Up (Fractions) Calculator Free. [1] [2] [3] [4]
Ch 9.3: Multiplying and Dividing Rational Expressions
Algebra Section 11-1 : Rational Expressions and Functions
Appendix A.4 Rational Expression.
Multiplying and Dividing Rational Expressions
Which fraction is the same as ?
6.6 Simplifying Rational Expressions
Rational Expressions and Equations
Algebra 1 Section 13.5.
Rational Expressions.
SLOT Week 11 – Day 1.
ALGEBRA II HONORS/GIFTED - SECTION 8-4 (Rational Expressions)
Unit 3: Rational Expressions Dr. Shildneck September 2014
Concept 5 Rational expressions.
10.3 Dividing Rational Expressions
SIMPLIFYING RATIONAL EXPRESSIONS & DOMAIN
Presentation transcript:

Algebra 11-3 and 11-4

Simplifying Rational Expressions A rational expression is an algebraic fraction whose numerator and denominator are polynomials (Can’t have ZERO in the denominator)

Example 1

Factor to Simplify Example 2

TRICKY– Recognize opposites Example 5

Rational Functions – find the zeros Example 6

Multiplying and Dividing Rational Expressions Same as any fraction, multiply numerators and multiply denominators When dividing, multiply by the RECIPROCAL!!!

Example 1

Example 3