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Solving Rational Equations

Solving Rational Equations. Example. Flashback (Lecture 3). Example Problem. Cross Multiply. Distribute Out. Solve. 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. WARNING.

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Solving Rational Equations

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  1. Solving Rational Equations

  2. Example

  3. Flashback (Lecture 3)

  4. Example Problem

  5. Cross Multiply

  6. Distribute Out

  7. Solve

  8. 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

  9. WARNING • Whenever you multiply both sides by something with an x in it, you risk creating an extra incorrect answer.

  10. Example 2

  11. 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

  12. Solve for x: x = 2 b) x = 2/3 c) x = 1/2 d) x = 1 e) None of the above

  13. Solve for x: D) x=1

  14. Solve for m: • m= k/2-1/p • m= (3pk)/(2p-k) • m= (3pk)/(k-2p) • m= (-3pk)/(p+k) • None of the choices are correct.

  15. C

  16. Solving Radical Equations dude.

  17. Simple Example

  18. Simple Example

  19. Slightly more complicated example

  20. Slightly more complicated example

  21. Another example

  22. Simply as much as you can BEFORE YOU SQUARE

  23. Recap • Simplify to get the roots by themselves • (if you can) • Square both sides • Solve for x

  24. Sometimes you can’t simplify first

  25. 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.

  26. Simple Example

  27. Slightly more complicated example

  28. Slightly more complicated example

  29. 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

  30. Find the solution(s): • x= 121/25 • x= 25/121 • x=25 • x=121 • No solutions

  31. A

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