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Worksheet: Extraneous Solutions for Rational Equations

Q1:

For what value of π‘Ÿ does the equation 2 π‘₯ + 5 π‘₯ βˆ’ 3 = π‘Ÿ have no solutions?

Q2:

Consider the equation

If you multiply both sides by π‘₯ βˆ’ 9  and rearrange so that the right-hand side is 0, what equation do you get?

  • A π‘₯ βˆ’ 3 = 0
  • B 0 = 0
  • C π‘₯ + 3 = 0
  • D 1 2 = 0
  • E π‘₯ βˆ’ π‘₯ βˆ’ 6 = 0 

What can you say about the solutions of the original equation?

  • Athere are two solutions
  • Bthere is only one solution
  • Cevery value of π‘₯ is a solution
  • Dthere are no solutions