Rational Function, Extraneous solution

Slides:

Advertisements

Similar presentations

Solving Rational Equations

Advertisements

Quiz Simplify. 8-6 Solve Rational Equations.

Algebraic Fractions and Rational Equations. In this discussion, we will look at examples of simplifying Algebraic Fractions using the 4 rules of fractions.

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

Ch 8 - Rational & Radical Functions 8.5 – Solving Rational Equations.

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,

Objectives: 1.Be able to solve a radical equation. 2.Be able to solve an equation that contains a rational exponent. Critical Vocabulary: Rational Exponents,

10.6 Solving Rational Equations

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

Quiz Simplify Solve 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:

Objectives: 1.Be able to determine if an equation is a rational equation. 2.Be able to solve various rational equations and exclude any extraneous solutions.

Simplify a rational expression

Solving Rational Equations Section 7.5 beginning on page 392.

Joyce DuVall Green Valley High School Henderson, Nevada.

Be sure to check all solutions for extraneous roots!

10-7 Solving Rational Equations Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview.

Rational Equations Section 8-6.

Prerequisite Skills VOCABULARY CHECK 40 ANSWER What is the least common denominator of and ? Which equation is a direct variation equation,

Add or subtract with like denominators

Challenge Problem! Work in your groups to do this problem:

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

Rational Numbers & Equations Lesson 3-5. Rational Numbers & Equations When given an equation with a fraction… a)Solve by multiplying by the reciprocal.

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

EQUATIONS & INEQUALITIES

9-6 SOLVING RATIONAL EQUATIONS & INEQUALITIES Objectives: 1) The student will be able to solve rational equations. 2) The student will be able to solve.

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.

Section 8.5 Solving Equations Containing Rational Expressions.

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

Advanced Algebra H Notes Section 8.6-Solving Rational Equations Objective: To be able to solve a rational equation. Rational Equations You can use ____________________to.

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

9.6 Solving Rational Equations Algebra II w/trig.

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

Holt Algebra Solving Rational Equations Warm Up 1. Find the LCM of x, 2x 2, and Find the LCM of p 2 – 4p and p 2 – 16. Multiply. Simplify.

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?

Rational Expressions and Functions: Adding and Subtracting

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

8.6 Solving Rational Equations

EQUATIONS & INEQUALITIES

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

Rational Function, Extraneous solution

Rational Function, Extraneous solution

9.6 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

Notes Over 9.6 An Equation with One Solution

Algebra 1 Section 13.6.

4.2: Solving Rational Equations

11-5 Solving Rational Equations

Rational Expressions and Equations

8.5 Solving Rational Equations

Solving Rational Equations

Warm-Up Simplify..

8.5 Solving Rational Equations

Rational Equations.

31. Solving Rational Equations

9.6 Solving Rational Equations

Section 11.8 Day 1 Rational Equations

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

Rational Function, Extraneous (excluded values) solutions

Objective Standard 15.0 I will solve a rational equation by multiplying the LCM of the denominators to both sides.

8.5 Solving Rational Equations

11-5 Solving Rational Equations

Presentation transcript:

Rational Function, Extraneous solution Objectives: Be able to solve various rational equations and exclude any extraneous solutions. Critical Vocabulary: Rational Function, Extraneous solution

II. Solving Rational Equations a. Solving a Rational: Cross Multiplication (Proportion) 1. First determine what “x” can’t be (6t + 7)(2t - 4) = (4t - 1)(3t + 8) Cross Multiply 12t2 - 10t - 28 = 12t2 + 29t - 8 FOIL -10t - 28 = 29t - 8 What are talking about? What is an extraneous solution? -39t - 28 = -8 -39t = 20 Solution: x = -20/39 That’s where your solution is one of the values that “x” can’t be. Look like you didn’t get any extraneous solutions.

This is not an extraneous solution either. II. Solving Rational Equations b. Solving a Rational: By Finding LCM (Denominator) 2. What can x not be? Multiply by LCD Distribute 6 + 8x = 7 8x = 1 This is not an extraneous solution either. Solution: x = 1/8 No….really?

3. II. Solving Rational Equations What can x not be? Multiply by LCD 3x + 2(x - 1) = 3 Distribute 3x + 2x - 2 = 3 This means there is no solution 5x - 2 = 3 5x = 5 x = 1 This is extraneous. What does that mean? Solution: None

II. Solving Rational Equations 4. Factor Denominators 2x = 4 - (x - 2) 2x = 4 - x + 2 3x = 6 x = 2 Solution: None