Download - Solving Rational Equations
![Page 1: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/1.jpg)
Solving Rational Equations
![Page 2: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/2.jpg)
Example
![Page 3: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/3.jpg)
Flashback (Lecture 3)
![Page 4: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/4.jpg)
Example Problem
![Page 5: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/5.jpg)
Cross Multiply
![Page 6: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/6.jpg)
Distribute Out
![Page 7: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/7.jpg)
Solve
![Page 8: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/8.jpg)
Recap
• Add fractions to get a single denominator on each side
• Cross multiply to get rid of denominators• Combine like terms and solve for x
![Page 9: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/9.jpg)
WARNING
• Whenever you multiply both sides by something with an x in it, you risk creating an extra incorrect answer.
![Page 10: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/10.jpg)
Example 2
![Page 11: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/11.jpg)
Recap
• Add fractions to get a single denominator on each side
• Cross multiply to get rid of denominators• Combine like terms and solve for x• Plug in and check for extra (wrong)
answers
![Page 12: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/12.jpg)
Solve for x:
a) x = 2
b) x = 2/3
c) x = 1/2
d) x = 1
e) None of the above
![Page 13: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/13.jpg)
Solve for x:
D) x=1
![Page 14: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/14.jpg)
Solve for m:
a) m= k/2-1/p
b) m= (3pk)/(2p-k)
c) m= (3pk)/(k-2p)
d) m= (-3pk)/(p+k)
e) None of the choices are correct.
pmk
132
![Page 15: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/15.jpg)
C
![Page 16: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/16.jpg)
Solving Radical Equations
dude.
![Page 17: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/17.jpg)
Simple Example
![Page 18: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/18.jpg)
Simple Example
![Page 19: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/19.jpg)
Slightly more complicated example
![Page 20: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/20.jpg)
Slightly more complicated example
![Page 21: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/21.jpg)
Another example
![Page 22: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/22.jpg)
Simply as much as you can BEFORE YOU SQUARE
![Page 23: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/23.jpg)
Recap
• Simplify to get the roots by themselves – (if you can)
• Square both sides• Solve for x
![Page 24: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/24.jpg)
Sometimes you can’t simplify first
![Page 25: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/25.jpg)
WARNING
• Whenever you square both sides, you’re multiplying both sides by something with an x in it.
• Whenever you multiply both sides by something with an x in it, you risk creating an extra incorrect answer.
![Page 26: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/26.jpg)
Simple Example
![Page 27: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/27.jpg)
Slightly more complicated example
![Page 28: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/28.jpg)
Slightly more complicated example
![Page 29: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/29.jpg)
Recap
• Simplify to get the roots by themselves – (if you can)
• Square both sides• Solve for x• Plug in and check for extra incorrect
answers
![Page 30: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/30.jpg)
Find the solution(s):
a) x= 121/25
b) x= 25/121
c) x=25
d) x=121
e) No solutions
xx 35
![Page 31: Solving Rational Equations](https://reader035.vdocuments.us/reader035/viewer/2022062217/56814d51550346895dba896b/html5/thumbnails/31.jpg)
A