## Reflection: Real World Applications Rational Expressions & Equations - Section 2: Practice working with Rational Expressions

The question might be asked, "Wouldn't it be better to have some real-world application for these problems?"

We've seen in the Cell Phone problem that rational functions do arise in the real world, so the utility of these functions is clear.  However, now it seems that it's important to consider them as mathematical objects in their own right, to study them in their natural habitat, so to speak.  Later, we'll be able to take this deep conceptual understanding back into the real world.

On another note, I've used the analogy of "false positives" in my explanation of extraneous solutions.  Perhaps that needs some explanation.

When solving these equations, we are often left at the end of the process with two different x-values.  Ordinarily, we'd move forward with confidence to say that there are two solutions.  But our faith in the algebraic process has been shaken; we know that sometimes one of these apparent solutions is really a fake.

Our algebraic solution process has ruled out all numbers except these two.  What if we ruled out a number that actually is a solution?  That would be a "false negative" result.  What if we failed to rule out a number that actually is not a solution?  That would be a "false positive", an extraneous solution.  We know for sure that we sometimes get a false positive.  How can we be certain that our solution process never results in a false negative?

Thoughts on the Content
Real World Applications: Thoughts on the Content

# Rational Expressions & Equations

Unit 7: Rational Functions
Lesson 7 of 17

## Big Idea: Examining the structure of an equation before solving it helps students avoid pitfalls and recognize extraneous solutions.

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Standards:
Subject(s):
Math, rational expressions, Algebra, rational equations, Simplifying Equations and Expressions, Function Operations and Inverses, Algebra 2, master teacher project, discontinuity, extraneous solutions
45 minutes

### Jacob Nazeck

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