Worksheet: Extraneous Solutions for Rational Equations

In this worksheet, we will practice determining extraneous solutions of rational equations.

Q1:

For what value of 𝑟 does the equation 2 𝑥 + 5 𝑥 3 = 𝑟 have no solutions?

Q2:

Consider the equation

If you multiply both sides by 𝑥 9 and rearrange so that the right-hand side is 0, what equation do you get?

  • A 𝑥 3 = 0
  • B 0 = 0
  • C 𝑥 + 3 = 0
  • D 1 2 = 0
  • E 𝑥 𝑥 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 𝑥 is a solution
  • Dthere are no solutions

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