Read page 254 Example 2 in your textbook, Principles of Mathematics 12.

Complete the Your Turn questions on page 254 (both equations) to practice solving equations with no solutions.

Click here to verify your answers.

Now that you have had an opportunity to practice solving and verifying rational equations, look at some word problems.

Watch the videos below to see how to use a rational equation to model and solve a problem.

Applying Rational Equations 1

Applying Rational Equations 2

Complete the following questions related to these videos.

Hold your mouse over the following questionsto verify your answers.

If you have any difficulty with these solutions, please contact your teacher before continuing.


  1. In Applying Rational Equations 1, the narrator refers to «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mfrac»«mn»8«/mn»«mn»15«/mn»«/mfrac»«mo»=«/mo»«mfrac»«mn»1«/mn»«mi»t«/mi»«/mfrac»«/mrow»«/mstyle»«/math» says you can “flip” both sides. What is another way to explain the work for this step?
    To eliminate the fractions, you can cross multiply.

    «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mfrac»«mn»8«/mn»«mn»15«/mn»«/mfrac»«menclose notation=¨downdiagonalstrike updiagonalstrike¨»«mo»=«/mo»«/menclose»«mfrac»«mn»1«/mn»«mi»t«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn»8«/mn»«mo»§#215;«/mo»«mi»t«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»15«/mn»«mo»§#215;«/mo»«mn»1«/mn»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn»8«/mn»«mi»t«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»15«/mn»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»t«/mi»«mo»=«/mo»«mfrac»«mn»15«/mn»«mn»8«/mn»«/mfrac»«/mrow»«/mstyle»«/math»


  2. Why does the narrator start both solutions by defining variables?
    The narrator starts by defining the variables because you must have defined variables to use in building your equation. If the variables are not defined, then the meaning of the equation is not clear.