## Reflection: Complex Tasks Solving Rational Equations - Section 2: Solving Rational Equations

As my students worked on these problems the other day, I noticed a few things that I thought were worth sharing.

First of all, I was really happy to see that the extraneous solutions weren't giving them any trouble at all.  By identifying the excluded values of x at the very beginning, it "just made sense" that they might have to toss out one of their solutions.

At the same time, however, I was a bit dismayed to see how many students struggled to apply the Quadratic Formula to problem 1b without error.  Time and again, I had to point to this problem and say something like, "I think you'd better double-check this one."  This is one of those cases in which they know how to solve it, but they can't seem to carry out the arithmetic without making mistakes along the way.

Problem 1c is an interesting case.  Only a few students noticed that they could eliminate the (x-2) denominator.  The rest found themselves stuck with a cubic polynomial and weren't sure how to solve it.  In the end, I asked one of these students to present his solution to the class so everyone could see how to simplify the equation before attempting to solve it.

Similarly, there were many mistakes as students tried to simplify expression 2b.  That said, they were pretty excited to see how simple it became in the end.  At one point, many students were "done" with this problem, but they all had different answers.  I asked for a volunteer to explain her solution at the board.  Before long, it turned into a whole-class discussion as everyone recognized one mistake or another in their own work.  By the end, everyone was engaged, and we'd had a chance to discuss quite a few errors and misconceptions.

Difficulties to Watch For
Complex Tasks: Difficulties to Watch For

# Solving Rational Equations

Unit 7: Rational Functions
Lesson 8 of 17

## Big Idea: Examining the structure of the equation makes it easier for students to identify and understand extraneous solutions.

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Standards:
Subject(s):
Math, Graphing (Algebra), Algebra, rational equations, Function Operations and Inverses, Algebra 2, master teacher project, extraneous solutions
50 minutes

### Jacob Nazeck

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