EXAMPLE 3 Simplify an expression by dividing out binomials Simplify x 2 – 3x – 10 x 2 + 6x + 8. State the excluded values. SOLUTION x 2 – 3x – 10 x 2 +

Slides:

Advertisements

Similar presentations

Operations on Rational Expressions Review

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.

Factor out a common binomial EXAMPLE 1 2x(x + 4) – 3(x + 4) a. SOLUTION 3y 2 (y – 2) + 5(2 – y) b. 2x(x + 4) – 3(x + 4) = (x + 4)(2x – 3) a. The binomials.

Warm Up Simplify each expression. Factor the expression.

Rational Expressions, Vertical Asymptotes, and Holes.

Chapter 7 - Rational Expressions and Functions

Rational Expressions Simplifying. Simplifying Rational Expressions The objective is to be able to simplify a rational expression.

Multiply complex numbers

EXAMPLE 1 Solve a simple absolute value equation Solve |x – 5| = 7. Graph the solution. SOLUTION | x – 5 | = 7 x – 5 = – 7 or x – 5 = 7 x = 5 – 7 or x.

Class Greeting. Chapter 7 Rational Expressions and Equations Lesson 7-1a Simplifying Rational Expressions.

Holt Algebra Simplifying Rational Expressions Warm Up Simplify each expression Factor each expression. 3. x 2 + 5x x 2 – 64 (x + 2)(x.

Solve a radical equation

Example 3 Dividing Mixed Numbers ÷ – 3 19 = 17 6 – Multiply by the reciprocal of 17 6 – 6 – = 3 () 6 – 19 Use rule for multiplying fractions.

Rational Expressions Simplifying Algebra B.

Do Now: Pass out calculators. Work on EOC Review Week # 21. Have your agenda out with your assignments written down for a scholar dollar and your current.

Warm ups. Find the sum or difference SOLVING RATIONAL EXPRESSIONS AND REVIEW Objective: To review adding, subtracting, and solving rational expressions.

Notes Over 9.4 Simplifying a Rational Expression Simplify the expression if possible. Rational Expression A fraction whose numerator and denominator are.

3.9 Multiplying & Dividing Rational Expressions p

3.7 Warm Up Solve the equation. 1. √(x + 3) + 8 = √(8 – 3x) + 5 = √(2x + 1) – 7 = 1.

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.

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

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

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

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)

Rational Expressions Simplifying Section Simplifying Rational Expressions The objective is to be able to simplify a rational expression.

Warm-up Factor each polynomial. 1. 4x 2 – 6x2. 15y y 3. n 2 + 4n p 2 – p – 42.

3.10 Warm Up Do # 4, 8, & 12 on pg. 268 Do # 4, 8, & 12 on pg. 268.

Add & Subtract Rationals – Common Denominator To add or subtract rational expressions with common denominators: 1) Add or subtract the numerators 2) Write.

Divide a polynomial by a binomial

8 4 Multiply & Divide Rational Expressions

12.5 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Multiply and Divide Rational Expressions.

EXAMPLE 3 Add expressions with different denominators Find the sum 5 12x 3 9 8x28x x28x2 += 9 3x 8x 2 3x x 3 2 Rewrite fractions using LCD,

Section 6.4 Rational Equations

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

SOLUTION Divide a polynomial by a monomial EXAMPLE 1 Divide 4x 3 + 8x x by 2x. Method 1 : Write the division as a fraction. Write as fraction. Divide.

EXAMPLE 5 Simplify a rational model 46 – 2.2x C = 100 – 18x + 2.2x 2 where x is the number of years since Rewrite the model so that it has only whole.

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

EXAMPLE 4 Rewrite polynomials Divide 5y + y by 2 + y. Rewrite polynomials. Multiply y and y + 2. y 2 + 2y Subtract y 2 + 2y. Bring down 4. 3y + 4.

3.8 Simplifying Rational Expressions p Vocabulary Rational Expression: ratio of 2 polynomials Rational Expression: ratio of 2 polynomials Excluded.

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

Factor out a common binomial

11.6 Adding and Subtracting Rational Expressions

12.4 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Simplify Rational Expressions.

9.6 Solving Rational Equations and Inequalities. Solve the Rational Equation Check your Solution What is the Common Denominator of 24, 4 and (3 – x) 4.

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.

Patel – Honors Classes Only Page 243 # Factoring Polynomials 2/6/14 Thursday.

Holt Algebra Dividing Polynomials Warm Up Divide. 1. m 2 n ÷ mn x 3 y 2 ÷ 6xy 3. (3a + 6a 2 ) ÷ 3a 2 b Factor each expression. 4. 5x x.

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.

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)

Add and Subtract Rational Expressions

Simplifying Rational Expressions Section 11.3.

Simplifying Rational Expressions

8.1 Multiplying and Dividing Rational Expressions

Multiplying and Dividing Rational Expressions

EXAMPLE 1 Find excluded values

Warm Up Lesson Presentation Lesson Quiz

8.4 Multiply & Divide Rational Expressions

Have out to be checked: P. 680/14-23 all, 29; Don't graph 22 and 23.

Without a calculator, simplify the expressions:

Mult/Divide Rational Expressions

Algebra Section 11-1 : Rational Expressions and Functions

Which fraction is the same as ?

11-1 Simplifying Rational Expressions

6.7 Dividing a Polynomial by a Polynomial

Algebra 1 Section 13.3.

Adding and Subtracting Rational Expressions

Presentation transcript:

EXAMPLE 3 Simplify an expression by dividing out binomials Simplify x 2 – 3x – 10 x 2 + 6x + 8. State the excluded values. SOLUTION x 2 – 3x – 10 x 2 + 6x + 8 = (x – 5)(x + 2) (x + 4)(x + 2) Factor numerator and denominator. (x – 5)(x + 2) (x + 4)(x + 2) = = x – 5 x + 4 Divide out common factor. Simplify. ANSWER The excluded values are – 4 and – 2.

EXAMPLE 3 Simplify an expression by dividing out binomials CHECK In the graphing calculator activity on page 560, you saw how to use a graph to check a sum or difference of polynomials. Check your simplification using a graphing calculator. Graph y 1 x 2 – 3x – 10 x 2 + 6x + 8 and y 2 = = x – 5 x + 4 The graphs coincide. So, the expressions are equivalent for all values of x other than the excluded values (– 4 and – 2 ).

EXAMPLE 4 Recognize opposites Simplify x 2 – 7x – x 2. State the excluded values. SOLUTION x 2 – 7x – x 2 Factor numerator and denominator. (x – 3)(x – 4) – (x – 4)(4 + x) = Rewrite 4 – x as – ( x – 4). Simplify. – (x – 4)(4+ x) (x – 3)(x – 4) = Divide out common factor. –(4 + x) (x – 3) = (x – 3)(x – 4) (x – 4)(4 + x) = ANSWER The excluded values are – 4 and 4. (x + 4) (x – 3) = –

GUIDED PRACTICE for Examples 3 and 4 Simplify the rational expression. State the excluded values. 9. x 2 + 3x + 2 x 2 + 7x + 10 (x + 1) (x + 5) ANSWER The excluded values are – 2 and – y 2 – 64 y 2 – 16y + 64 ANSWER (y + 8) (y – 8) The excluded value is z – z 2 z 2 – 3z – 10 ANSWER (z + 1) (z + 2) – The excluded values are 5 and – 2.