SlideShare a Scribd company logo
1 of 13
Download to read offline
Still Working
Those Equations




                  Derivative Works by flickr user widdowquinn
You know how to multiply
 binomials right?

(x + 1)(x - 3) then (x + 1)(x - 3)



 And how to factor
 trinomials?

       x 2- 2x -3
Fast Math to multiply numbers
 You know how to multiply
                                         -- 2 Digit Numbers
 binomials right?

(x + 1)(x - 3) then (x + 1)(x - 3)



 And how to factor
 trinomials?

       x 2- 2x -3
               What does this:




                                     http://www.youtube.com/watch?v=9qQAYEYLCoU
have to do with that?
To solve rational equations, follow
these steps:
1. Remove the denominators of the rational expressions by
multiplying each rational expression in the equation by the least
common denominator.
    For example, the least common denominator of the equation



                                    is
To solve rational equations, follow
these steps:
2. Multiply each term by the least common denominator (e.g., 6x(x – 1))
to yield an equation with all denominators equal to 1.




                       x=3 x=4
To solve rational equations, follow
these steps:
 3. Check your possible solution(s) for x. Check that neither of these
 numbers will cause any of the original denominators to equal 0.

 Since the restrictions are x≠1 and x≠0 it follows that x = 3 or x = 4
 are the solutions to the original equation.
`
    To solve rational equations, follow
    these steps:

    Note: Be careful not
    to confuse a rational
    expression and a
    rational equation.



    When simplifying a rational expression, the
    denominator remains (unless it cancels with a
    common factor in the numerator).


                  In solving a rational equation, the denominator is cleared by
                  multiplying both sides by the least common denominator.
Solve and state restrictions if any ...
                                           Solving
                                          Equations
Solve and state restrictions if any ...
                                           Solving
                                          Equations
Solve and state restrictions if any ...
                                           Solving
                                          Equations
Solve and state restrictions if any ...
                                           Solving
                                          Equations
Solve and state restrictions if any ...
                                           Solving
                                          Equations
Solve and state restrictions if any ...
                                           Solving
                                          Equations

More Related Content

What's hot

January 29, 2014
January 29, 2014January 29, 2014
January 29, 2014
khyps13
 
Solving systems of linear equations by substitution
Solving systems of linear equations by substitutionSolving systems of linear equations by substitution
Solving systems of linear equations by substitution
duanenestor
 
Solving systems of equations in 3 variables
Solving systems of equations in 3 variablesSolving systems of equations in 3 variables
Solving systems of equations in 3 variables
Jessica Garcia
 

What's hot (19)

Diffy Q Paper
Diffy Q PaperDiffy Q Paper
Diffy Q Paper
 
Consistency of linear equations in two and three variables
Consistency of linear equations in two and three variablesConsistency of linear equations in two and three variables
Consistency of linear equations in two and three variables
 
7.1
7.17.1
7.1
 
Intro
IntroIntro
Intro
 
Differential equation and Laplace transform
Differential equation and Laplace transformDifferential equation and Laplace transform
Differential equation and Laplace transform
 
Advance engineering mathematics
Advance engineering mathematicsAdvance engineering mathematics
Advance engineering mathematics
 
Ordinary differential equation
Ordinary differential equationOrdinary differential equation
Ordinary differential equation
 
Problem space
Problem spaceProblem space
Problem space
 
Scse 1793 Differential Equation lecture 1
Scse 1793 Differential Equation lecture 1Scse 1793 Differential Equation lecture 1
Scse 1793 Differential Equation lecture 1
 
January 29, 2014
January 29, 2014January 29, 2014
January 29, 2014
 
Lu decomposition
Lu decompositionLu decomposition
Lu decomposition
 
Solving systems of linear equations by substitution
Solving systems of linear equations by substitutionSolving systems of linear equations by substitution
Solving systems of linear equations by substitution
 
Solving Systems of Linear Equation using Substitution method
Solving Systems of Linear Equation using Substitution methodSolving Systems of Linear Equation using Substitution method
Solving Systems of Linear Equation using Substitution method
 
Solving systems of equations in 3 variables
Solving systems of equations in 3 variablesSolving systems of equations in 3 variables
Solving systems of equations in 3 variables
 
How to solve linear equations by substitution
How to solve linear equations by substitutionHow to solve linear equations by substitution
How to solve linear equations by substitution
 
Variational Principle
Variational PrincipleVariational Principle
Variational Principle
 
Ch03 1
Ch03 1Ch03 1
Ch03 1
 
Sect1 3
Sect1 3Sect1 3
Sect1 3
 
Systems of 3 Equations in 3 Variables
Systems of 3 Equations in 3 VariablesSystems of 3 Equations in 3 Variables
Systems of 3 Equations in 3 Variables
 

Similar to Pre-Cal 20S December 17, 2008

119 powerpoint 1.2
119 powerpoint 1.2119 powerpoint 1.2
119 powerpoint 1.2
Jeneva Clark
 
M098 outcomes and assessment matrix
M098 outcomes and assessment matrixM098 outcomes and assessment matrix
M098 outcomes and assessment matrix
chairsty
 
May 28, 2014
May 28, 2014May 28, 2014
May 28, 2014
khyps13
 
Solving rational expressions
Solving rational expressionsSolving rational expressions
Solving rational expressions
Jessica Garcia
 
Solving rational expressions
Solving rational expressionsSolving rational expressions
Solving rational expressions
Jessica Garcia
 
5.7 Quadratic Inequalities
5.7 Quadratic Inequalities5.7 Quadratic Inequalities
5.7 Quadratic Inequalities
hisema01
 

Similar to Pre-Cal 20S December 17, 2008 (20)

Pre-Cal 20S December 16, 2008
Pre-Cal 20S December 16, 2008Pre-Cal 20S December 16, 2008
Pre-Cal 20S December 16, 2008
 
119 powerpoint 1.2
119 powerpoint 1.2119 powerpoint 1.2
119 powerpoint 1.2
 
quadratic equations-1
quadratic equations-1quadratic equations-1
quadratic equations-1
 
1.1 Linear and Literal Equations
1.1 Linear and Literal Equations1.1 Linear and Literal Equations
1.1 Linear and Literal Equations
 
.
..
.
 
First Order Differential Equations
First Order Differential EquationsFirst Order Differential Equations
First Order Differential Equations
 
Lecture 01 - Linear Equations.ppt
Lecture 01 - Linear Equations.pptLecture 01 - Linear Equations.ppt
Lecture 01 - Linear Equations.ppt
 
M098 outcomes and assessment matrix
M098 outcomes and assessment matrixM098 outcomes and assessment matrix
M098 outcomes and assessment matrix
 
May 28, 2014
May 28, 2014May 28, 2014
May 28, 2014
 
Solving rational expressions
Solving rational expressionsSolving rational expressions
Solving rational expressions
 
Solving rational expressions
Solving rational expressionsSolving rational expressions
Solving rational expressions
 
Algebra solving no animations
Algebra   solving no animationsAlgebra   solving no animations
Algebra solving no animations
 
Theory of Equation
Theory of EquationTheory of Equation
Theory of Equation
 
Linear equations
Linear equationsLinear equations
Linear equations
 
Linear equations
Linear equationsLinear equations
Linear equations
 
Solving inequalities that involve radical functions (Nov 28, 2013)
Solving inequalities that involve radical functions (Nov 28, 2013) Solving inequalities that involve radical functions (Nov 28, 2013)
Solving inequalities that involve radical functions (Nov 28, 2013)
 
Classification of solutions
Classification of solutionsClassification of solutions
Classification of solutions
 
5.7 Quadratic Inequalities
5.7 Quadratic Inequalities5.7 Quadratic Inequalities
5.7 Quadratic Inequalities
 
Linear Equations
Linear EquationsLinear Equations
Linear Equations
 
Solve systemsbygraphing
Solve systemsbygraphingSolve systemsbygraphing
Solve systemsbygraphing
 

More from Darren Kuropatwa

More from Darren Kuropatwa (20)

Behind Their Eyes v1
Behind Their Eyes v1Behind Their Eyes v1
Behind Their Eyes v1
 
Leading Change v1
Leading Change v1Leading Change v1
Leading Change v1
 
Providing Permission To Wonder v2.1
Providing Permission To Wonder v2.1Providing Permission To Wonder v2.1
Providing Permission To Wonder v2.1
 
Things That Suck About Digital Citizenship v1
Things That Suck About Digital Citizenship v1Things That Suck About Digital Citizenship v1
Things That Suck About Digital Citizenship v1
 
Digital Storytelling for Deeper Learning v1
Digital Storytelling for Deeper Learning v1Digital Storytelling for Deeper Learning v1
Digital Storytelling for Deeper Learning v1
 
Tales of Learning and the Gifts of Footprints v4.2
Tales of Learning and the Gifts of Footprints v4.2Tales of Learning and the Gifts of Footprints v4.2
Tales of Learning and the Gifts of Footprints v4.2
 
The Fourth Screen v4.2
The Fourth Screen v4.2The Fourth Screen v4.2
The Fourth Screen v4.2
 
Making Student Thinking Visible v4
 Making Student Thinking Visible v4 Making Student Thinking Visible v4
Making Student Thinking Visible v4
 
Learning is at BYTE 2017
Learning is at BYTE 2017Learning is at BYTE 2017
Learning is at BYTE 2017
 
Leveraging Digital for Deeper Learning
Leveraging Digital for Deeper LearningLeveraging Digital for Deeper Learning
Leveraging Digital for Deeper Learning
 
We Learn Through Stories at PRIZMAH17
We Learn Through Stories at PRIZMAH17We Learn Through Stories at PRIZMAH17
We Learn Through Stories at PRIZMAH17
 
Providing Permission to Wonder v3
Providing Permission to Wonder v3Providing Permission to Wonder v3
Providing Permission to Wonder v3
 
The Fourth Screen v4.1
The Fourth Screen v4.1The Fourth Screen v4.1
The Fourth Screen v4.1
 
Making Student Thinking Visible v3.7
 Making Student Thinking Visible v3.7 Making Student Thinking Visible v3.7
Making Student Thinking Visible v3.7
 
Learning is at AUHSD
Learning is at AUHSDLearning is at AUHSD
Learning is at AUHSD
 
Providing Permission to Wonder v2
Providing Permission to Wonder v2Providing Permission to Wonder v2
Providing Permission to Wonder v2
 
The Fourth Screen v4
The Fourth Screen v4The Fourth Screen v4
The Fourth Screen v4
 
Learning is at BLC16
Learning is at BLC16Learning is at BLC16
Learning is at BLC16
 
We Learn Through Stories v4 (master class)
We Learn Through Stories v4 (master class)We Learn Through Stories v4 (master class)
We Learn Through Stories v4 (master class)
 
Deep Learning Design: the middle ring
Deep Learning Design: the middle ringDeep Learning Design: the middle ring
Deep Learning Design: the middle ring
 

Recently uploaded

Recently uploaded (20)

Data Cloud, More than a CDP by Matt Robison
Data Cloud, More than a CDP by Matt RobisonData Cloud, More than a CDP by Matt Robison
Data Cloud, More than a CDP by Matt Robison
 
Scaling API-first – The story of a global engineering organization
Scaling API-first – The story of a global engineering organizationScaling API-first – The story of a global engineering organization
Scaling API-first – The story of a global engineering organization
 
Apidays Singapore 2024 - Building Digital Trust in a Digital Economy by Veron...
Apidays Singapore 2024 - Building Digital Trust in a Digital Economy by Veron...Apidays Singapore 2024 - Building Digital Trust in a Digital Economy by Veron...
Apidays Singapore 2024 - Building Digital Trust in a Digital Economy by Veron...
 
Boost Fertility New Invention Ups Success Rates.pdf
Boost Fertility New Invention Ups Success Rates.pdfBoost Fertility New Invention Ups Success Rates.pdf
Boost Fertility New Invention Ups Success Rates.pdf
 
Advantages of Hiring UIUX Design Service Providers for Your Business
Advantages of Hiring UIUX Design Service Providers for Your BusinessAdvantages of Hiring UIUX Design Service Providers for Your Business
Advantages of Hiring UIUX Design Service Providers for Your Business
 
ProductAnonymous-April2024-WinProductDiscovery-MelissaKlemke
ProductAnonymous-April2024-WinProductDiscovery-MelissaKlemkeProductAnonymous-April2024-WinProductDiscovery-MelissaKlemke
ProductAnonymous-April2024-WinProductDiscovery-MelissaKlemke
 
Tech Trends Report 2024 Future Today Institute.pdf
Tech Trends Report 2024 Future Today Institute.pdfTech Trends Report 2024 Future Today Institute.pdf
Tech Trends Report 2024 Future Today Institute.pdf
 
Handwritten Text Recognition for manuscripts and early printed texts
Handwritten Text Recognition for manuscripts and early printed textsHandwritten Text Recognition for manuscripts and early printed texts
Handwritten Text Recognition for manuscripts and early printed texts
 
Bajaj Allianz Life Insurance Company - Insurer Innovation Award 2024
Bajaj Allianz Life Insurance Company - Insurer Innovation Award 2024Bajaj Allianz Life Insurance Company - Insurer Innovation Award 2024
Bajaj Allianz Life Insurance Company - Insurer Innovation Award 2024
 
Driving Behavioral Change for Information Management through Data-Driven Gree...
Driving Behavioral Change for Information Management through Data-Driven Gree...Driving Behavioral Change for Information Management through Data-Driven Gree...
Driving Behavioral Change for Information Management through Data-Driven Gree...
 
Connector Corner: Accelerate revenue generation using UiPath API-centric busi...
Connector Corner: Accelerate revenue generation using UiPath API-centric busi...Connector Corner: Accelerate revenue generation using UiPath API-centric busi...
Connector Corner: Accelerate revenue generation using UiPath API-centric busi...
 
Tata AIG General Insurance Company - Insurer Innovation Award 2024
Tata AIG General Insurance Company - Insurer Innovation Award 2024Tata AIG General Insurance Company - Insurer Innovation Award 2024
Tata AIG General Insurance Company - Insurer Innovation Award 2024
 
Workshop - Best of Both Worlds_ Combine KG and Vector search for enhanced R...
Workshop - Best of Both Worlds_ Combine  KG and Vector search for  enhanced R...Workshop - Best of Both Worlds_ Combine  KG and Vector search for  enhanced R...
Workshop - Best of Both Worlds_ Combine KG and Vector search for enhanced R...
 
Understanding Discord NSFW Servers A Guide for Responsible Users.pdf
Understanding Discord NSFW Servers A Guide for Responsible Users.pdfUnderstanding Discord NSFW Servers A Guide for Responsible Users.pdf
Understanding Discord NSFW Servers A Guide for Responsible Users.pdf
 
Apidays New York 2024 - The value of a flexible API Management solution for O...
Apidays New York 2024 - The value of a flexible API Management solution for O...Apidays New York 2024 - The value of a flexible API Management solution for O...
Apidays New York 2024 - The value of a flexible API Management solution for O...
 
Apidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, Adobe
Apidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, AdobeApidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, Adobe
Apidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, Adobe
 
Exploring the Future Potential of AI-Enabled Smartphone Processors
Exploring the Future Potential of AI-Enabled Smartphone ProcessorsExploring the Future Potential of AI-Enabled Smartphone Processors
Exploring the Future Potential of AI-Enabled Smartphone Processors
 
How to Troubleshoot Apps for the Modern Connected Worker
How to Troubleshoot Apps for the Modern Connected WorkerHow to Troubleshoot Apps for the Modern Connected Worker
How to Troubleshoot Apps for the Modern Connected Worker
 
Strategize a Smooth Tenant-to-tenant Migration and Copilot Takeoff
Strategize a Smooth Tenant-to-tenant Migration and Copilot TakeoffStrategize a Smooth Tenant-to-tenant Migration and Copilot Takeoff
Strategize a Smooth Tenant-to-tenant Migration and Copilot Takeoff
 
2024: Domino Containers - The Next Step. News from the Domino Container commu...
2024: Domino Containers - The Next Step. News from the Domino Container commu...2024: Domino Containers - The Next Step. News from the Domino Container commu...
2024: Domino Containers - The Next Step. News from the Domino Container commu...
 

Pre-Cal 20S December 17, 2008

  • 1. Still Working Those Equations Derivative Works by flickr user widdowquinn
  • 2. You know how to multiply binomials right? (x + 1)(x - 3) then (x + 1)(x - 3) And how to factor trinomials? x 2- 2x -3
  • 3. Fast Math to multiply numbers You know how to multiply -- 2 Digit Numbers binomials right? (x + 1)(x - 3) then (x + 1)(x - 3) And how to factor trinomials? x 2- 2x -3 What does this: http://www.youtube.com/watch?v=9qQAYEYLCoU have to do with that?
  • 4. To solve rational equations, follow these steps: 1. Remove the denominators of the rational expressions by multiplying each rational expression in the equation by the least common denominator. For example, the least common denominator of the equation is
  • 5. To solve rational equations, follow these steps: 2. Multiply each term by the least common denominator (e.g., 6x(x – 1)) to yield an equation with all denominators equal to 1. x=3 x=4
  • 6. To solve rational equations, follow these steps: 3. Check your possible solution(s) for x. Check that neither of these numbers will cause any of the original denominators to equal 0. Since the restrictions are x≠1 and x≠0 it follows that x = 3 or x = 4 are the solutions to the original equation.
  • 7. ` To solve rational equations, follow these steps: Note: Be careful not to confuse a rational expression and a rational equation. When simplifying a rational expression, the denominator remains (unless it cancels with a common factor in the numerator). In solving a rational equation, the denominator is cleared by multiplying both sides by the least common denominator.
  • 8. Solve and state restrictions if any ... Solving Equations
  • 9. Solve and state restrictions if any ... Solving Equations
  • 10. Solve and state restrictions if any ... Solving Equations
  • 11. Solve and state restrictions if any ... Solving Equations
  • 12. Solve and state restrictions if any ... Solving Equations
  • 13. Solve and state restrictions if any ... Solving Equations