9.3 Simplifying and Multiplying Rational Expressions

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

Copyright © Cengage Learning. All rights reserved.

9.1 Multiplying and Dividing Rational Expressions

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

Warm-up Given these solutions below: write the equation of the polynomial: 1. {-1, 2, ½)

Rational Expressions.

Simplify Rational Expressions

R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

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)

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.

3.8 Simplify Rational ExpressionsVocabulary An expression that can be written as a ratio of two polynomials. Rational Expression A number that makes a.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 7 Rational Expressions and Equations.

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

Rational Expressions – Sum & Difference 1 When fractions already have a common denominator, keep the denominator the same and add / subtract your numerators.

3.8 Warm Up 1. (18x³ - 24x² + 12x) ∕ 6x 2. (5x² + 7x – 6) ∕ (x + 2) 3. (9x² + 5x – 6) ∕ (x + 1)

Chapter 12 Final Exam Review. Section 12.4 “Simplify Rational Expressions” A RATIONAL EXPRESSION is an expression that can be written as a ratio (fraction)

Bell Ringer 9/18/15 1. Simplify 3x 6x 2. Multiply 1 X Divide 2 ÷

5.6 Solving Quadratic Function By Finding Square Roots 12/14/2012.

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

4.1 Properties of Exponents

GOAL: USE PROPERTIES OF RADICALS AND RATIONAL EXPONENTS Section 7-2: Properties of Rational Exponents.

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

Copyright © Cengage Learning. All rights reserved. 7 Rational Functions.

Simplify, Multiply & Divide Rational Expressions.

Rational Functions. Do Now Factor the following polynomial completely: 1) x 2 – 11x – 26 2) 2x 3 – 4x 2 + 2x 3) 2y 5 – 18y 3.

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

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 _

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

EXAMPLE 2 Simplify expressions by dividing out monomials Simplify the rational expression, if possible. State the excluded values. a. r 2r SOLUTION Divide.

Warm-up Answers:. Homework Answers: P3 (55-58 all, all, odds, all) /1690.

Chapter 7 Section 4 Rational Exponents. A rational exponent is another way to write a radical expression. Like the radical form, the exponent form always.

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.

Chapter 11.2 Notes: Simplify Rational Expressions Goal: You will simplify rational expressions.

Section 6.1 Rational Expressions Definition A rational expression is the ratio of two polynomials. Examples:

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?

Lesson 8.2 Notes Quotient of Powers- to divide two powers that have the same base, subtract the exponents – Ex: Power of a Quotient- to find the power.

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.

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

Simplifying Rational Expressions Section 11.3.

Simplifying Rational Expressions

Apply Exponent Properties Involving Quotients

7.4: Add and subtract rational exp.

8.1 Multiplying and Dividing Rational Expressions

Rational expressions 8.11.

7.1/7.2 – Rational Expressions: Simplifying, Multiplying, and Dividing

Multiplying and Dividing Rational Expressions

EXAMPLE 1 Find excluded values

Rational Expressions and Equations

8.4 Multiply & Divide Rational Expressions

Multiply and Divide Rational Expressions

Adding and subtracting rational expressions

Section 8-2: Multiplying and Dividing Rational Expressions

Mult/Divide Rational Expressions

Simplify Complex Rational Expressions

Adding and subtracting rational expressions

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

Find the product or quotient.

9.4: Rational Expressions

6.6 Simplifying Rational Expressions

ALGEBRA II HONORS/GIFTED - SECTION 8-4 (Rational Expressions)

Presentation transcript:

9.3 Simplifying and Multiplying Rational Expressions 4/13/2014

Rational Expression: an expression that is the ratio of two polynomials. It is "Rational" because one is divided by the other, like a ratio. the polynomial you are dividing by cannot be zero. Note: Ex:

Simplify the rational expression, if possible. Example 1 Simplify a Rational Expression Simplify the rational expression, if possible. 15x = • 3 5 x 5 Divide out the common factor 5 and simplify. a. =3𝑥 5 b. x x 5 + This expression is already in simplest form. c. 14x2 6x 2 7 x x = • 2 3 x Divide out the common factors 2 and x. = 3 7𝑥 3

Simplify the expression, if possible. Checkpoint Simplify a Rational Expression Simplify the expression, if possible. 4x ANSWER 2x 5 1. 10 2. 8 4x ANSWER 2 x 9x ( 12 1 x + 3. ANSWER 3x ( 4 1 x + x 1 – 4. ANSWER already in simplest form

Simplify the expression, if possible. Checkpoint Write in Simplest Form Simplify the expression, if possible. 2x 1 + 5. ANSWER already in simplest form 6. 3x ( ) 1 x + 3x 2 ANSWER x ( ) 1 +

Simplify the expression, if possible. Checkpoint Write in Simplest Form Simplify the expression, if possible. 2x 2 + 8x 7. 12x ANSWER 6 4 x + 8. 2 x + 6 3x ANSWER 3 1

Multiply . Simplify the result. • 3x 8x 5 Example 3 Multiply Rational Expressions 4x 2 9x Multiply . Simplify the result. • 3x 8x 5 SOLUTION 3x 4x 2 9x • 8x 5 1 3 1 2 = 3 𝑥 2 2 𝑥 5 Subtract exponents of x = 2x 3 3 7

Multiply . Simplify the result. • x x 2 9 – 4x 3x 12 Example 4 Multiply Rational Expressions Multiply . Simplify the result. • x x 2 9 – 4x 3x 12 SOLUTION • x x 2 9 – 4x 3x 12 Factor the numerators and denominators. = 4 3x ( ) 3 x – + • = 4 ( ) 3 x + 8

Multiply the rational expressions. Simplify the result. Checkpoint Multiply Rational Expressions Multiply the rational expressions. Simplify the result. 9. 14 3x 7x • 6x 3 ANSWER 4x 1 • x 2 2x 4 – 3x 6 10. ANSWER 3x 4 • x 2 6x 4 – 11. 4x 8 + x 3 ANSWER 24 x 2 ( ) 2 x –

Multiply . Simplify the result. • 3 ( 2 – x ( Example 5 Multiply by a Polynomial x x 2 – 6 5x + Multiply . Simplify the result. • 3 ( 2 – x ( SOLUTION • x x 2 + 5x 6 ( 2 – 3 Write polynomial as a rational expression. = • 1 x x 2 + 5x 6 ( 2 – 3 Factor out of . 1 – ( 2 x = • x 2 3 Simplify. = x – 3x 3 10

Multiply the expressions. Simplify the result. Checkpoint Multiply by a Polynomial Multiply the expressions. Simplify the result. x + 4 12. 2x ( • 3 6 ANSWER 8 x 13. 3x + x 2 ( • 12 4x ANSWER x 2 3 3x 14. x 2 • – ( 2 x ANSWER x 3x – + 1

Homework: 9.3 p.483 #22-52 even only I’m reading a book about anti-gravity. I can’t put it down!!!