Rational Equations Section 8-6.

Slides:

Advertisements

Similar presentations

Solving 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,

Solving Equations with the Variable on Both Sides Objectives: to solve equations with the variable on both sides.

EXAMPLE 4 Solve proportions SOLUTION a x 16 = Multiply. Divide each side by 10. a x 16 = = 10 x5 16 = 10 x80 = x8 Write original proportion.

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

Solve an equation with variables on both sides

EXAMPLE 2 Using the Cross Products Property = 40.8 m Write original proportion. Cross products property Multiply. 6.8m 6.8 = Divide.

Using Cross Products Lesson 6-4. Cross Products When you have a proportion (two equal ratios), then you have equivalent cross products. Find the cross.

How to solve using cross multiplication Created by: Brittany and Andrea.

Standardized Test Practice

Warm-up Find the domain and range from these 3 equations.

10.6 Solving Rational Equations

Solving Exponential and Logarithmic Equations Section 8.6.

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

Solving Rational Equations

EXAMPLE 2 Rationalize denominators of fractions Simplify

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

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

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

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 12 Final Exam Review. Section 12.4 “Simplify Rational Expressions” A RATIONAL EXPRESSION is an expression that can be written as a ratio (fraction)

5.6 Solving Quadratic Function By Finding Square Roots 12/14/2012.

Use the Distributive Property to: 1) simplify expressions 2) Solve equations.

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

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

Monday Schedule Monday: Rational Equations Tuesday: Rational Equations Wednesday: In class Activity, Factoring Quiz Thursday: Quiz Friday:

Practice 2.2 Solving Two Step Equations.

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

Solve Linear Systems by Substitution January 28, 2014 Pages

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

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

Multiplication and Division Properties. Multiplication Properties Commutative Property Associative Property Identity Property Zero Property Distributive.

2.2 Solving Two- Step Equations. Solving Two Steps Equations 1. Use the Addition or Subtraction Property of Equality to get the term with a variable on.

Equations with fractions can be simplified by multiplying both sides by a common denominator. 3x + 4 = 2x + 8 3x = 2x + 4 x = 4 Example: Solve

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:

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.

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

Solving Equations with Variables on Both Sides. Review O Suppose you want to solve -4m m = -3 What would you do as your first step? Explain.

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.

Section 8.5 and 8.6 Multiplying and Dividing Radicals/Solving Radical Equations.

Solve the equation. 1. = 4 x x(x – 4) = 3(x – 4) + x ANSWER 10

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

5.8 Radical Equations and Inequalities

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

EXAMPLE 2 Rationalize denominators of fractions Simplify

Solving Equations with the Variable on Each Side

Notes 7.1 Day 1– Solving Two-Step Equations

Rational Expressions and Equations

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

Find the least common multiple for each pair.

9.6 Solving Rational Equations

Solving 1-Step Integer Equations

Find the least common multiple for each pair.

Algebra 1 Section 13.6.

4.2: Solving Rational Equations

Rational Expressions and Equations

8.5 Solving Rational Equations

Solving Multiplication Equations

8.5 Solving Rational Equations

Rational Equations.

Definition of logarithm

8.5 Solving Rational Equations

11-5 Solving Rational Equations

EXAMPLE 4 Solve proportions Solve the proportion. ALGEBRA a x 16

Using Cross Products Chapter 3.

Presentation transcript:

Rational Equations Section 8-6

Objectives Solve rational equations with one variable by CROSS MULTIPLYING Check answers for Extraneous Solutions

Extraneous Solutions Any solution that makes a denominator ZERO does not check. (Extraneous)

Solving Rational Equations Two basic methods 1. Cross Multiply two rational expressions to solve them 2. Set equation equal to ZERO and then get Common Denominator

Today Cross Multiplying Method

Cross Multiplication Method

Example 2

Example 3

Solve a rational equation by cross multiplying EXAMPLE 1 Solve a rational equation by cross multiplying Solve: 3 x + 1 = 9 4x + 1 3 x + 1 = 9 4x + 1 Write original equation. 3(4x + 5) = 9(x + 1) Cross multiply. 12x + 15 = 9x + 9 Distributive property 3x + 15 = 9 Subtract 9x from each side. 3x = – 6 Subtract 15 from each side. x = – 2 Divide each side by 3. The solution is –2. Check this in the original equation. ANSWER

Homework WS 12-5