8.4 Multiply and Divide Rational Expressions

Slides:

Advertisements

Similar presentations

10-10 Complex Rational Expressions Standard 13.0 Standard 13.0 One Key Term One Key Term.

Advertisements

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.

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.

Dividing Rational Expressions Use the following steps to divide rational expressions. 1.Take the reciprocal of the rational expression following the division.

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

In multiplying rational expressions, we use the following rule: Dividing by a rational expression is the same as multiplying by its reciprocal. 5.2 Multiplying.

Adding & Subtracting Rational Expressions. Vocabulary Rational Expression Rational Expression - An expression that can be written as a ratio of 2 polynomials.

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)

Aim: How do we multiply and divide rational expressions?

Section 9-3a Multiplying and Dividing Rational Expressions.

 Multiply rational expressions.  Use the same properties to multiply and divide rational expressions as you would with numerical fractions.

9.5 Adding and Subtracting Rational Expressions 4/23/2014.

EXAMPLE 2 Multiply rational expressions involving polynomials Find the product 3x 2 + 3x 4x 2 – 24x + 36 x 2 – 4x + 3 x 2 – x Multiply numerators and denominators.

Operations on Rational Expressions. Rational expressions are fractions in which the numerator and denominator are polynomials and the denominator does.

Warm up # (-24) =4.) 2.5(-26) = 2-7(-8)(-3) = 5.) -5(9)(-2) = 3.

MULTIPLY and DIVIDE RATIONAL NUMBERS. MULTPILYING MIXED NUMBERS 1)Change all Mixed numbers to improper fractions 2)Simplify A) Up and Down B) Diagonally.

10/24/ Simplifying, Multiplying and Dividing Rational Expressions.

§ 7.2 Multiplying and Dividing Rational Expressions.

11.4 Multiply and Divide Rational Expressions. SIMPLIFYING RATIONAL EXPRESSIONS Step 1: Factor numerator and denominator “when in doubt, write it out!!”

9.4 Multiplying and Dividing Rational Expressions -To multiply and divide rational expressions. -Use rational expressions to model real life quantities.

8 4 Multiply & Divide Rational Expressions

Multiplying and Dividing Rational Expressions

Simplify, Multiply & Divide Rational Expressions.

9.4 Multiply and Divide Rational Expressions VOCABULARY Simplified form of a rational expression.

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

Table of Contents Dividing Rational Expressions Use the following steps to divide rational expressions. 1.Take the reciprocal of the rational expression.

Do Now Pass out calculators. Have your homework out ready to check.

9.3 Simplifying and Multiplying Rational Expressions 4/26/2013.

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.

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.

Factor the expression x – 5x2 3. x3 – 125 ANSWER 5x (2 – x)

Objectives  Perform operations with rational expressions in a real-world example.  Add, subtract, multiply, and divide rational expressions. Page 546.

Objectives Add and subtract rational expressions.

How do we multiply and divide Rational Expressions?

Simplifying, Multiplying, and Dividing

6.8 Multiplying and Dividing Rational Expressions

Multiplying and Dividing Rational Expressions

Do Now: Multiply the expression. Simplify the result.

Multiplying and Dividing Fractions

Simplify each expression. Assume all variables are nonzero.

8.4 Multiply and Divide Rational Expressions

Simplify each expression. Assume all variables are nonzero.

Simplifying Rational Expressions

8.1 Multiplying and Dividing Rational Expressions

Multiplying and Dividing Rational Expressions

8.4 Multiply & Divide Rational Expressions

Multiplying and Dividing Rational Expressions

Multiplying and Dividing Rational Expressions

Bell Work: 11/6/14 Simplify the following numeric fractions

Without a calculator, simplify the expressions:

Add and Subtract Rational Expressions

Mult/Divide Rational Expressions

Simplify Complex Rational Expressions

Warm-Up (Fractions) Calculator Free. [1] [2] [3] [4]

Simplify each expression. Assume all variables are nonzero.

Simplifying rational expressions

Dividing Fractions and Mixed Numbers

Multiplying and Dividing Rational Expressions

Rational Expressions and Equations

Divide Rational Expressions

Multiplying and Dividing Rational Expressions

SLOT Week 11 – Day 1.

Unit 3: Rational Expressions Dr. Shildneck September 2014

10.3 Dividing Rational Expressions

Presentation transcript:

8.4 Multiply and Divide Rational Expressions VOCABULARY Simplified form of a rational expression

VOCABULARY Simplified form of a rational expression A rational expression in which its numerator and denominator have no common factors (other than ±1 )

SIMPLIFYING RATIONAL EXPRESSIONS Step 1: Factor numerator and denominator Step 2: Divide out common factors Step 3: Simplified form

Example 1 Simplify a rational expression (x² + 7x + 10) (x² - 4) Step 1: Factor numerator and denominator (x² + 7x + 10) = (x+2)(x+5) (x² - 4) (x+2)(x-2) Step 2: Divide out common factor (x+2)(x+5) (x+2)(x-2) Step 3: Simplified Form (x+5) (x-2)

Checkpoint Simplify the expression x² - 2x – 15 x² + 4x + 3 (x – 5)(x + 3) (x + 1)(x + 3) (x – 5) (x + 1)

MULTIPLYING RATIONAL EXPRESSIONS Step 1: Factor numerators and denominators Step 2: Multiply numerators and denominators Step 3: Divide out common factors Step 4: Simplified form

Example 2 Multiply rational expressions 2x² + 4x x² - 9x + 18 x² - 4x – 12 * 2x Step 1: Factor 2x(x + 2) (x – 3)(x – 6) (x + 2)(x – 6) * 2x Step 2: Multiple 2x(x + 2)(x – 3)(x – 6) (x + 2)(x – 6)2x

2x² + 4x x² - 9x + 18 x² - 4x – 12 * 2x Step 3: Divide Step 4: Simplify x – 3

Checkpoint Multiply the expression 6x² + 18x x² - x – 2 x² + x – 6 * x² - 7x – 8 6x(x + 3) (x-2)(x+1) (x+3)(x-2) * (x-8)(x+1) 6x(x + 3)(x-2)(x+1) (x+3)(x-2)(x-8)(x+1) 6x (x-8)

Example 3 Multiply a rational expression by a polynomial x – 4 * (x² - x + 1) x³ + 1 x³ + 1 1 (x-4)(x² - x + 1) (x+1)( x² - x + 1) X – 4 X + 1

Dividing Rational Expressions Step 1: Multiply by reciprocal Step 2: Factor Step 3: Divide Step 4: Simplify

Example 4 Divide rational expressions 3 ÷ 8x² - 8x x + 7 x² + 6x – 7 Step 1: keep, change, flip 3 x² + 6x – 7 x+7 * 8x² - 8x Step 2: Factor 3 (x+7)(x-1) (x+7)(8x)(x-1)

3 ● 8x² - 8x x + 7 ● x² + 6x – 7 cont. Step 3: Divide 3 (x+7)(x-1) Step 4: Simplify 3__ 8x

Checkpoint Divide the expression 3. x – 5 ● 2x² - 11x + 5 9x² - 18x ● 2x² - 5x + 2 (x – 5) (2x² - 5x + 2) (9x² - 18x)(2x² - 11x + 5) (x – 5)(2x-1)(x-2) 9x(x–2)(2x-1)(x-5) 1_ 9x

Source 8.4 Multiply and Divide Rational Expressions 8.4 Multiply and Divide Rational Expressions simpsonmath.wikispaces.com/file/view/8.4+notes.ppt Retrieved March 12, 2012