1. Lesson 3

1.7. Explore 3

Mathematics 30-1 Module 7

Module 7: Rational Functions and Function Operations

 

When solving a rational equation, it is common to come across extraneous roots. Try This 3 explores this idea.

 

Try This 3


Tyrone and Kalina are trying to solve

 

Tyrone used an algebraic approach and wrote the following steps:

 

 

 

Kalina decided to use a graphical approach and made this graph. She agreed with Tyrone’s solution, as the functions on her graph looked as though they could possibly intersect at about x = 3 as the functions continued.

 

This graph shows the function f at x equals 15 divided by all of x times x minus 3, and then all plus 4 divided by x. It also shows the function g at x equals 5 divided by all of x minus 3.

  1. Substitute x = 3 into to check that it is a solution.
  2. What error did Tyrone make?
  3. What error did Kalina make?
  4. What should Tyrone and Kalina have stated as the solution to ? Explain.
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The algebra of Tyrone’s solution is correct.