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Solving rational expressions

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Jessica Garcia
Jessica Garcia

The document provides instructions and examples for solving rational equations and inequalities. It explains that rational equations can be solved by multiplying both sides by the least common denominator to eliminate fractions. Students are advised to check their solutions and watch out for extraneous solutions. The steps for solving rational inequalities are given as identifying domain restrictions, moving everything to one side, solving, and drawing vertical lines to indicate intervals on the number line. Some sample problems are worked through as examples.

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9.6 Solving Rational Equations p.505
Hint for solving: ,[object Object],[object Object],[object Object]
Example : Solve. LCD : 2x Multiply each fraction through by the LCD Check your solution!
Solve. LCD : ? LCD : (x+1) Check your solution! ? No Solution!
Solve. Factor 1 st ! LCD: (x+2)(x-2) Check your solutions!
Short Cut! ,[object Object]
Example : Solve. Check your solutions!
Last Example : Solve. Check your solutions!
Solve for x (alternate method): Multiply through by a common denominator to get rid of all fractions
Solving Rational Inequalities ,[object Object],[object Object],[object Object],[object Object]
Example ,[object Object],[object Object],[object Object],[object Object]
Example ,[object Object],[object Object],[object Object],[object Object]
SAT Question – Rational Expressions If and which of the following gives all values of x? ,[object Object],[object Object],[object Object],[object Object],[object Object]
One more SAT Question If Which of the following is an expression for
Now you try! Pg 509 #’s 6-9 all

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Solving rational expressions

  • 1. 9.6 Solving Rational Equations p.505
  • 2.
  • 3. Example : Solve. LCD : 2x Multiply each fraction through by the LCD Check your solution!
  • 4. Solve. LCD : ? LCD : (x+1) Check your solution! ? No Solution!
  • 5. Solve. Factor 1 st ! LCD: (x+2)(x-2) Check your solutions!
  • 6.
  • 7. Example : Solve. Check your solutions!
  • 8. Last Example : Solve. Check your solutions!
  • 9. Solve for x (alternate method): Multiply through by a common denominator to get rid of all fractions
  • 10.
  • 11.
  • 12.
  • 13.
  • 14. One more SAT Question If Which of the following is an expression for
  • 15. Now you try! Pg 509 #’s 6-9 all