October 31 st copyright2009merrydavidson. Simplifying Rational Expressions What is the difference between a factor and a term? TERMS are separated by.

Slides:

Advertisements

Similar presentations

Rational Algebraic Expressions

Advertisements

Objective SWBAT simplify rational expressions, add, subtract, multiply, and divide rational expressions and solve rational equations.

The Fundamental Property of Rational Expressions

Warm Up Simplify each expression. Factor the expression.

Chapter 7 - Rational Expressions and Functions

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

Rational Expressions Student will be able to simplify rational expressions And identify what values make the expression Undefined . a.16.

Homework Solution lesson 8.5

Solving Rational Equations A Rational Equation is an equation that contains one or more rational expressions. The following are rational equations:

1.1 Linear Equations A linear equation in one variable is equivalent to an equation of the form To solve an equation means to find all the solutions of.

Addition and Subtraction with Like Denominators Let p, q, and r represent polynomials where q ≠ 0. To add or subtract when denominators are the same,

Chapter 6 Section 6 Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solving Equations with Rational Expressions Distinguish between.

Rational Expressions Simplifying Algebra B.

Section R5: Rational Expressions

( ) EXAMPLE 3 Standardized Test Practice SOLUTION 5 x = – 9 – 9

6-2:Solving Rational Equations Unit 6: Rational and Radical Equations.

Chapter 6 Section 4 Addition and Subtraction of Rational Expressions.

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

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 =

 Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero.

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

Simplify a rational expression

Solving Rational Equations On to Section 2.8a. Solving Rational Equations Rational Equation – an equation involving rational expressions or fractions…can.

Chapter 11 Sections 11.1, 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)

11-9 Rational Equations and Functions Algebra 1 Glencoe McGraw-HillLinda Stamper.

Solving Equations with Rational Expressions Distinguish between operations with rational expressions and equations with terms that are rational expressions.

Solution Because no variable appears in the denominator, no restrictions exist. The LCM of 5, 2, and 4 is 20, so we multiply both sides by 20: Example.

How can we solve fractional equations? Do now: Solve for x What steps did you use to solve?

Rational Equations Section 8-6.

Holt McDougal Algebra 2 Solving Rational Equations and Inequalities Solving Rational Equations and Inequalities Holt Algebra 2Holt McDougal Algebra 2.

Copyright © Cengage Learning. All rights reserved. Rational Expressions and Equations; Ratio and Proportion 6.

Multi-Step Equations We must simplify each expression on the equal sign to look like a one, two, three step equation.

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

(x+2)(x-2).  Objective: Be able to solve equations involving rational expressions.  Strategy: Multiply by the common denominator.  NOTE: BE SURE TO.

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

Bell Work: Graph on a number line I x I > 0. Answer: All reals.

Solving Equations Containing First, we will look at solving these problems algebraically. Here is an example that we will do together using two different.

Rational Expressions Simplifying Rational Expressions.

Martin-Gay, Beginning Algebra, 5ed Solve the following rational equation.EXAMPLE Because no variable appears in the denominator, no restrictions.

9.4 Rational Expressions (Day 1). A rational expression is in _______ form when its numerator and denominator are polynomials that have no common factors.

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

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.

8.5 Solving Rational Equations. 1. Factor all denominators 2. Find the LCD 3.Multiply every term on both sides of the equation by the LCD to cancel out.

Add ___ to each side. Example 1 Solve a radical equation Solve Write original equation. 3.5 Solve Radical Equations Solution Divide each side by ___.

Aim: How do we solve fractional equations?

Chapter 6 Rational Expressions and Equations

Rational Expressions and Equations

Rational Expressions and Functions: Adding and Subtracting

Section R.6 Rational Expressions.

Chapter 8 Rational Expressions.

1. Add: 5 x2 – 1 + 2x x2 + 5x – 6 ANSWERS 2x2 +7x + 30

Simplifying Rational Expressions

( ) EXAMPLE 3 Standardized Test Practice SOLUTION 5 x = – 9 – 9

Find the least common multiple for each pair.

9.6 Solving Rational Equations

Solving Equations with the Variable on Both Sides

Rational Expressions and Equations

Solving Equations Containing

Warm Up Simplify each expression. 1. Factor each expression.

Find the least common multiple for each pair.

4.2: Solving Rational Equations

Rational Expressions and Equations

Rational Expressions and Equations

8.5 Solving Rational Equations

Rational Equations.

Solving Rational Equations and Inequalities

31. Solving Rational Equations

The Domain of an Algebraic Expression

Presentation transcript:

October 31 st copyright2009merrydavidson

Simplifying Rational Expressions What is the difference between a factor and a term? TERMS are separated by +, - signs. FACTORS are separated by multiplication sign. An expression has NO equal sign.

The REDUCTION PROPERTY OF FRACTIONS You are allowed to divide out (cancel) common factors (not common terms) that appear in both the numerator and the denominator. You may NOT cancel the “4x”’s. They are terms not factors!

Example 2: Can you cancel anything out? Why or Why not??? There are NO add or subtract signs so these are all factors. Reduce the 2/4 to ½ and cancel out the p’s. List domain restrictions. domain restrictions are called critical numbers.

CRITICAL NUMBERS: Found in the numerator by solving for x. C.N. = 3/2 Found in the denominator by solving for x. C.N. = ¾,-5

Example 3: SIMPLIFY: List domain restrictions. List critical numbers. DO domain restrictions and critical numbers before canceling.

Example 4: Can you cancel anything out? Why or Why not? These are all terms so no. Factor to see if anything will match to cancel. List domain restrictions. List critical numbers. SIMPLIFY:

Example 5: For this example only simplify and list answer with domain restrictions. Remember to do domain restrictions BEFORE canceling!!!

Example 6: (x – 5) and (5 – x) are opposites….. In order to cancel you must factor out a (-1) from one of those terms.

7. Solve the following rational equation. Step 1: Find the LCD. Step 2: Multiply each term by the LCD over 1. Step 3: Cancel Step 5: Solve the equation. LCD = Step 4: Re-write the equation. 3x + 4 = 42 x = 38/3

8. Solve the following rational equation. LCD is: (x + 1) + 4 = 6x 3x = 6x 7 = 3x 7/3 = x

Extraneous Solutions: You are not allowed to have a zero in the denominator of a fraction. Therefore, If you get x = 5 and 5 would make the denominator = 0, 5 would be an extraneous solution. In other words, if algebraically you get a solution, but that makes the denominator zero it is called an extraneous solution. For any fraction with a variable in the denominator you must list domain restrictions first (that is what x can not be).

9. Solve the following rational equation. There is a variable in the denominator. What can x not be? x = 0 LCD is 5x x = 65 By using the LCD and canceling you eliminate the denominator. 8x = 50 x = 25/4 Since the answer is not a domain restriction we are done.

10. Solve the following rational equation. List domain restrictions FIRST. Solve Check for extraneous solutions. x – = 2x - 5 x = 2x = x But x cannot be 5. the answer is: no real solution and 5 is extraneous.

11. Solve the following rational equation. Factor everything possible. domain restrictions: x = 0, -2, -1

LCD: (x + 1)(x + 1) – (x + 2)(x + 4) = -3x x 2 + 2x + 1 – x 2 – 6x - 8 = -3x x = -7 domain restrictions: x = 0, -2, -1

12. Solve the following rational equation. Be sure that everything in the denominator gets canceled out

12. 3x 2 – 13x + 4 – 3x – 3 = 2x 2 + x - 15 (x – 4)(3x – 1) – 3(x + 1) = (x + 3)(2x – 5) x 2 – 17x + 16 = 0 x = 1, 16

HW: WS 4-4