9-6 Solving Rational Equations

Slides:

Advertisements

Similar presentations

Quiz Simplify. 8-6 Solve Rational Equations.

Advertisements

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

Homework Solution lesson 8.5

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.

Solving equations Section 1.4.

10.6 Solving Rational Equations

Solving Rational Equations

4.2 Solving Rational Equations 1/30/2013. Vocabulary Rational Equation: Equation that shows two rational expressions or fractions are equal. Example:

Warm Up January 27, 2014 Simplify 1. Pick up handout on back table.

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

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)

Solving Rational Equations Section 7.5 beginning on page 392.

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

3.3 Equations w/ Variables on both sides. 3.3 – Eq. w/ Variables on both sides Goals / “I can…”  Solve equations with variables on both sides  Identify.

Example 1: a basic fraction problem from chapter 1 What is the common Denominator? Factor 3 2*3 2*2 3 * 2 * 2 = 12 You need the factors of every denominator.

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.

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

Math – Rational Equations 1. A rational equation is an equation that has one or more rational expressions in it. To solve, we start by multiplying.

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

Solving Rational Equations

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

Lesson 11-5 Warm-Up.

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

Essential Question: What must you do to find the solutions of a rational equation?

Copyright © 2011 Pearson, Inc. 2.7 Solving Equations in One Variable.

9.6 Solving Rational Equations p.569. Hint for solving: A quick way to solve a rational equation is to multiply everything through by the LCD. This will.

10.6 Solving Rational Equations Rational Equation An equation containing one or more rational expressions.

SAT Prep: Solving Rational Equations Goals: To solve problems involving rational expressions (equations that have variables in the denominator)

9.6 Solving Rational Equations 5/13/2013. Vocabulary Rational Equation: Equation that shows two rational expressions or fractions are equal. Example:

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

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.

Aim: How do we solve fractional equations?

6-3: Solving Equations with variables on both sides of the equal sign

8.6 Solving Rational Equations

Solving Rational Equations

EQUATIONS & INEQUALITIES

Solving Rational Equations

9.6 Solving Rational Equations

9.6 Solving Rational Equations

9.6 Solving Rational Equations

8.6 Solve Rational Equations

9.6 Solving Rational Equations

3.6 Clearing an Equation of Fractions and decimals

Equations with Algebraic Fractions

Solving Equations Containing Fractions

Fractional Equations Chapter 7 Section 7.4.

Solving Equations Containing

Warmups Simplify 1+ 2

Rational Equations.

Equations Containing Decimals

Algebra 1 Section 13.6.

4.2: Solving Rational Equations

11-5 Solving Rational Equations

Rational Expressions and Equations

8.5 Solving Rational Equations

Bell Ringer 12/6/18 1. What is the restriction on rational expressions which results in extraneous solutions? 2. When solving equations with fractions,

Solving Rational Equations

Warm-Up Simplify..

8.5 Solving Rational Equations

Rational Equations.

Solving Equations Containing Rational Expressions § 6.5 Solving Equations Containing Rational Expressions.

Solving Rational Equations

31. Solving Rational Equations

Example 2B: Solving Linear Systems by Elimination

9.6 Solving Rational Equations

Warm-up: Solve for x. Hint, factor first!.

8.5 Solving Rational Equations

11-5 Solving Rational Equations

Solving Systems of Linear Equations by Elimination

Presentation transcript:

9-6 Solving Rational Equations 3/27/17

To solve a rational EQ with a fraction on each side, cross-multiply to eliminate the fractions. Then solve the resulting EQ, but be sure to check for extraneous solutions. 4 x = 2x – 3 5 20 = 2x2 – 3x 0 = 2x2 – 3x – 20 0 = (2x + 5)(x – 4) x = -5/2 or 4

Combine fractions on one side 1st if you need to. 5 2 1 5 – = + 2x 3 x 6 15 4x 6 5x – = + 6x 6x 6x 6x Hey! The denom’s are all the same.. We can just ignore them and focus on the numerators! This is because we could multiply both sides by 6x, and this would clear all fractions. Just note that even if the “solution” is x = 0, it is NOT! x can not equal 0 because it is restricted.

TIP: Get an LCD for the whole problem, not just each side TIP: Get an LCD for the whole problem, not just each side. Then solve the EQ left by the numerators. 5 2 1 5 – = + 2x 3 x 6 15 4x 6 5x – = + 6x 6x 6x 6x 15 – 4x = 6 + 5x 15 = 6 + 9x 9 = 9x x = 1

Bob can drywall the room in 6 hours. Phil can drywall the room in 4 hours. Together they can drywall the room in ____ hours. h = # of hours How much of the room can Bob do in 1 hour? 1/6 of it How much of the room can Phil do in 1 hour? 1/4 of it What is their rate working together? (1/6 + 1/4) Equation: (1/6 + 1/4)h = 1 (5/12)h = 1 h = 12/5 = 2.4 hours

Assignment: Page 514 #1 – 5, 12 – 16, 24