6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2...
Transcript of 6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2...
![Page 1: 6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2 November 14, 2016 To solve an equation that involves fractions, one method is of solving](https://reader036.fdocuments.us/reader036/viewer/2022071002/5fbf10d0796b9a5a4c34c748/html5/thumbnails/1.jpg)
6.4_Rational_Equations.notebook
1
November 14, 2016
Focus On ...
Chapter 6 6.4 Rational Equations
• identifying nonpermissible values in a rational equation• determining the solution to a rational equation algebraically• solving problems using a rational equation
![Page 2: 6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2 November 14, 2016 To solve an equation that involves fractions, one method is of solving](https://reader036.fdocuments.us/reader036/viewer/2022071002/5fbf10d0796b9a5a4c34c748/html5/thumbnails/2.jpg)
6.4_Rational_Equations.notebook
2
November 14, 2016
To solve an equation that involves fractions, one method is of solving is to eliminate the denominator by multiplying through by the LCD (Lowest common denominator)
Example - Solve
We will use this to solve complicated rational equations
![Page 3: 6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2 November 14, 2016 To solve an equation that involves fractions, one method is of solving](https://reader036.fdocuments.us/reader036/viewer/2022071002/5fbf10d0796b9a5a4c34c748/html5/thumbnails/3.jpg)
6.4_Rational_Equations.notebook
3
November 14, 2016
6.4Example 1
Solve a Rational EquationSolve the following equation. What values are nonpermissible?
Continue Next Page
![Page 4: 6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2 November 14, 2016 To solve an equation that involves fractions, one method is of solving](https://reader036.fdocuments.us/reader036/viewer/2022071002/5fbf10d0796b9a5a4c34c748/html5/thumbnails/4.jpg)
6.4_Rational_Equations.notebook
4
November 14, 2016
1) Factor Denominators
2) State nonpermissible values
3) Determine Lowest Common Denominator
4) Multiply every term on both sides by the LCD to....
eliminate all of the denominators
5) Solve the resulting equation. (It may be linear or quadratic)
6) Compare solution to n.p.v, to make sure it isn't extraneous
The Steps
![Page 5: 6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2 November 14, 2016 To solve an equation that involves fractions, one method is of solving](https://reader036.fdocuments.us/reader036/viewer/2022071002/5fbf10d0796b9a5a4c34c748/html5/thumbnails/5.jpg)
6.4_Rational_Equations.notebook
5
November 14, 2016
![Page 6: 6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2 November 14, 2016 To solve an equation that involves fractions, one method is of solving](https://reader036.fdocuments.us/reader036/viewer/2022071002/5fbf10d0796b9a5a4c34c748/html5/thumbnails/6.jpg)
6.4_Rational_Equations.notebook
6
November 14, 2016
2 Multiply each term on both sides of the equation by 6( z – 2)(z + 2).
1 1
1 1
1 1
1 1
1
1
1 Factor each denominator.
z ≠–2, 2
![Page 7: 6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2 November 14, 2016 To solve an equation that involves fractions, one method is of solving](https://reader036.fdocuments.us/reader036/viewer/2022071002/5fbf10d0796b9a5a4c34c748/html5/thumbnails/7.jpg)
6.4_Rational_Equations.notebook
7
November 14, 2016
Check:Substitute z = 5 into the original equation.
Right SideLeft Side
Left Side = Right Side
3
![Page 8: 6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2 November 14, 2016 To solve an equation that involves fractions, one method is of solving](https://reader036.fdocuments.us/reader036/viewer/2022071002/5fbf10d0796b9a5a4c34c748/html5/thumbnails/8.jpg)
6.4_Rational_Equations.notebook
8
November 14, 2016
6.4
Example 1: Your Turn
Answer y ≠ 3, 6; y = 12
Solve the equation. What are the nonpermissible values?
1) Factor Denominators
2) State nonpermissible values
3) Determine Lowest Common Denominator
4) Multiply each term on both sides by
the LCD to eliminate all of the denominators5) Solve the resulting equation.
6) Compare solution to n.p.v, to make sure it isn't extraneous
![Page 9: 6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2 November 14, 2016 To solve an equation that involves fractions, one method is of solving](https://reader036.fdocuments.us/reader036/viewer/2022071002/5fbf10d0796b9a5a4c34c748/html5/thumbnails/9.jpg)
6.4_Rational_Equations.notebook
9
November 14, 2016
![Page 10: 6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2 November 14, 2016 To solve an equation that involves fractions, one method is of solving](https://reader036.fdocuments.us/reader036/viewer/2022071002/5fbf10d0796b9a5a4c34c748/html5/thumbnails/10.jpg)
6.4_Rational_Equations.notebook
10
November 14, 2016
6.4Example 2Solve a Rational Equation With an Extraneous RootSolve the equation. What are the nonpermissible values?
Continue Next Page
1) Factor Denominators
2) State nonpermissible values
3) Determine Lowest Common Denominator
4) Multiply each term on both sides by
the LCD to eliminate all of the denominators5) Solve the resulting equation.
6) Compare solution to n.p.v, to make sure it isn't extraneous
![Page 11: 6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2 November 14, 2016 To solve an equation that involves fractions, one method is of solving](https://reader036.fdocuments.us/reader036/viewer/2022071002/5fbf10d0796b9a5a4c34c748/html5/thumbnails/11.jpg)
6.4_Rational_Equations.notebook
11
November 14, 2016
![Page 12: 6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2 November 14, 2016 To solve an equation that involves fractions, one method is of solving](https://reader036.fdocuments.us/reader036/viewer/2022071002/5fbf10d0796b9a5a4c34c748/html5/thumbnails/12.jpg)
6.4_Rational_Equations.notebook
12
November 14, 2016
1 Factor any factorable terms in the equation.
k ≠ –2, 22
1
11
1
1
1
11
Multiply each term by (k – 2)(k + 2)
![Page 13: 6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2 November 14, 2016 To solve an equation that involves fractions, one method is of solving](https://reader036.fdocuments.us/reader036/viewer/2022071002/5fbf10d0796b9a5a4c34c748/html5/thumbnails/13.jpg)
6.4_Rational_Equations.notebook
13
November 14, 2016
4 Check: Substitute k = 6 into the original equation.
Left Side Right Side
Left Side = Right Side
Therefore, the solution is k = 6.
3 –2 is a nonpermissible value and is called an extraneous solution.
![Page 14: 6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2 November 14, 2016 To solve an equation that involves fractions, one method is of solving](https://reader036.fdocuments.us/reader036/viewer/2022071002/5fbf10d0796b9a5a4c34c748/html5/thumbnails/14.jpg)
6.4_Rational_Equations.notebook
14
November 14, 2016
6.4
Example 2: Your Turn
Answer
Solve the equation. What are the nonpermissible values?
1) Factor Denominators
2) State nonpermissible values
3) Determine Lowest Common Denominator
4) Multiply each term on both sides by
the LCD to eliminate all of the denominators5) Solve the resulting equation.
6) Compare solution to n.p.v, to make sure it isn't extraneous
![Page 15: 6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2 November 14, 2016 To solve an equation that involves fractions, one method is of solving](https://reader036.fdocuments.us/reader036/viewer/2022071002/5fbf10d0796b9a5a4c34c748/html5/thumbnails/15.jpg)
6.4_Rational_Equations.notebook
15
November 14, 2016
![Page 16: 6.4 Rational Equations.notebook - Grade 11 Pre Calculus · 6.4_Rational_Equations.notebook 2 November 14, 2016 To solve an equation that involves fractions, one method is of solving](https://reader036.fdocuments.us/reader036/viewer/2022071002/5fbf10d0796b9a5a4c34c748/html5/thumbnails/16.jpg)
6.4_Rational_Equations.notebook
16
November 14, 2016