8.5: Adding and Subtracting Rational Expressions

Slides:

Advertisements

Similar presentations

Complex Rational Expressions

Advertisements

10-5 Addition and Subtraction: Unlike Denominators  Standard 13.0: Add and subtract rational expressions.

Section 6.1 Rational Expressions.

Rational Expressions To add or subtract rational expressions, find the least common denominator, rewrite all terms with the LCD as the new denominator,

MTH 092 Section 12.1 Simplifying Rational Expressions Section 12.2

5.3 Adding and Subtracting Rational Expressions BobsMathClass.Com Copyright © 2010 All Rights Reserved. 1 Procedure: To add or subtract fractions with.

Rational Expressions rational expression: quotient of two polynomials x2 + 3x x + 2 means (x2 + 3x - 10) ÷ (3x + 2) restrictions: *the denominator.

Section R5: Rational Expressions

10.4 Addition and Subtraction: Like Denominators Goal: to add and subtract rational expressions with like denominators.

6.1 The Fundamental Property of Rational Expressions Rational Expression – has the form: where P and Q are polynomials with Q not equal to zero. Determining.

Chapter 6 Section 4 Addition and Subtraction of Rational Expressions.

Adding, Subtracting, Multiplying, & Dividing Rational Expressions

Adding and Subtracting Rational Expressions

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

RATIONAL EXPRESSIONS. EVALUATING RATIONAL EXPRESSIONS Evaluate the rational expression (if possible) for the given values of x: X = 0 X = 1 X = -3 X =

RATIONAL EXPRESSIONS. Definition of a Rational Expression A rational number is defined as the ratio of two integers, where q ≠ 0 Examples of rational.

Warm Up Add or subtract –

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

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

Chapter 11 Sections 11.1, Rational Expressions.

Algebraic Manipulation. Amendments to worksheet  Pg 3 Example 2:  Pg 3 Example 3:

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)

Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.

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

4.8 – Solving Equations with Fractions

Warm Up Add or subtract x ≠ x ≠ –1, x ≠ 1 Simplify. Identify any x-values for which the expression is undefined –

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.

Objectives Add and subtract rational expressions.

R5 - 1 Class Problems (10/07/15): Sec. R.5 Due in 15 minutes. (Write the problem and solve.)  wire basket Determine the domain Write in lowest terms.

Chapter 6 Section 6 Solving Rational Equations. A rational equation is one that contains one or more rational (fractional) expressions. Solving Rational.

1/20/ :24 AM10.3 Multiplying and Dividing Expressions1 Simplify, Multiply and Divide Rational Expressions Section 8-2.

HW answers.. Warm-up Add or Subtract without using a calculator.

Warm-up 6-1 Lesson 6-1 Simplifying Rational Expressions.

Adding and subtracting rational expressions: To add or subtract rational expressions use the addition property: Taken from

Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.

Simplifying Radical Expressions Objective: Add, subtract, multiply, divide, and simplify radical expressions.

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

Fractional Expressions Section 1.4. Objectives Simplify fractional expressions. Multiply and divide fractional expressions. Add and subtract fractional.

8.2 Adding and Subtracting Rational Expressions Goal 1 Determine the LCM of polynomials Goal 2 Add and Subtract Rational Expressions.

Welcome to Algebra 2 Rational Equations: What do fractions have to do with it?

Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.

Objectives Add and subtract rational expressions.

11.5 Adding and Subtracting Rational Expressions

Rational Expressions and Equations

Section R.6 Rational Expressions.

Adding and Subtracting Rational Expressions

Warm Up Add or subtract –

Chapter 8 Rational Expressions.

Warm Up Add or subtract –

Simplify each expression. Assume all variables are nonzero.

Simplify each expression. Assume all variables are nonzero.

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

Rational Expressions and Equations

12.3 – Rational Expressions – Adding and Subtracting

Radical Operations Unit 4-3.

Warm Up Add or subtract –

8.5 Add and Subtract Rational Expressions

Multiplying and Dividing Expressions

Rational Expressions and Equations

Adding and subtracting rational expressions is similar to adding and subtracting fractions. To add or subtract rational expressions with like denominators,

Simplifying Complex Rational Expressions

Rational Expressions and Equations

Simplify each expression. Assume all variables are nonzero.

8.6: Solving Rational Equations

8.5: Adding and Subtracting Rational Expressions

Adding and Subtracting Rational Expressions

29. Add and Subtract Rational Expressions

Adding and Subtracting Rational Expressions

8.5 Solving Rational Equations

9.5 Addition, Subtraction, and Complex Fractions

Presentation transcript:

8.5: Adding and Subtracting Rational Expressions Worksheet Key 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Page 577 3) B 4) A 5) C 7) 9) 11) 13) 15) 17) 19) Must factor first 21) 25) 27) 29) 31) (x + 2)(x + 7) 33) 35) 37) 39) 41) 43) EP1) –(x + 7) EP2) –(x + 3) EP3) (x2 + 5x + 25)(2x – 1) EP4) 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

Adding & Subtracting Rational Expressions Section 8.5 Adding & Subtracting Rational Expressions 8.5: Adding and Subtracting Rational Expressions 1/13/2019 10:56 AM

8.5: Adding and Subtracting Rational Expressions Review Add (2/3) + (6/3) 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Example 1 Add 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Example 2 Subtract 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Your Turn Subtract 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

Steps of Add & Subtract Rational Expressions When given an equation, rewrite the fraction using the common denominator. Simplify by combining like terms of both the numerator and denominator. Multiply if needed and then simplify. Reduce to lowest terms up top. Do NOT distribute the bottom. Determine what values the variables cannot equal to. 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

Steps of Add & Subtract Rational Expressions Common Denominator Multiply Divide Cancel 1/13/2019 10:56 AM 8.4: Multiply and Divide Rational Expressions

8.5: Adding and Subtracting Rational Expressions Review What is the common denominator of 6 and 15? What is the common denominator of 3x and 9x2? 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Review Simplify (2/3) – (1/2) 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Example 3 Find the LCD of (x + 2) and (x – 2) 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Example 4 Find the LCD of t2 – t – 6 and t2 + 3t + 2 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Your Turn Find the LCD of (x – 4)2 and (3x – 12) 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Example 5 Solve and identify any x-values for which the expression is/are undefined. 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Your Turn Solve and identify any x-values for which the expression is/are undefined. 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Example 6 Simplify (7/6x) – (5/8x) 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Example 7 Simplify and define what x values is/are undefined What is the common denominator? 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Example 7 Simplify and define what x values is/are undefined Apply the missing factors to the numerator. 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Example 7 Simplify and define what x values is/are undefined Simplify. Distribute the top. 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Example 7 Simplify and define what x values is/are undefined Combine like terms. 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Example 7 Simplify and define what x values is/are undefined Define what x values is/are undefined 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Example 8 Simplify and define what x values is/are undefined 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Your Turn Simplify and define what x values is/are undefined 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Example 9 Simplify and define what x values is/are undefined What is the first step in factoring? 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Your Turn Simplify and define what x values is/are undefined 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Example 10 Simplify and define what x values is/are undefined What is the first step in factoring? 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Your Turn Simplify and define what x values is/are undefined 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Example 11 Simplify and define what x values is/are undefined of (x + 2)–2 – (x2 – 4)–1 Rewrite the problem 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Example 11 Simplify and define what x values is/are undefined of (x + 2)–2 – (x2 – 4)–1 Apply and Simplify 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Your Turn Simplify (x – y)–1 – (x + y)–1 and assume that all expressions are defined. 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions

8.5: Adding and Subtracting Rational Expressions Assignment Pg 586: 3-29 odd, 41 1/13/2019 10:56 AM 8.5: Adding and Subtracting Rational Expressions