## Reflection: Connection to Prior Knowledge Operations with Rational Expressions - Section 2: Overview and Practice

One of the biggest student misconceptions that I encounter when teaching this unit is multiple variations on this error: x^2 / (x^2 +5) = ⅕. Students have a hard time seeing the difference between terms and factors and will commonly confuse them, insisting that “canceling the x-squared” should work in the above example in the same way that it works here: 3x^2/5x^2 = ⅗.

To begin this unit, we recall the elementary school mathematics they learned about operations with fractions in order to generalize and create some rules regarding operations with rational expressions. This connection to prior learning is highly effective in creating a foundational understanding of what they are about to dive into, but it can still leave room for the above misconception to occur. I like to conclude our discussion of these rules with the following numerical examples: simplify 5/(5 + 4 + 2), simplify 5/(20 + 10), simplify 5/(5*(4 + 2)), simplify 5/(5*4 +2). Comparing and contrasting these examples can help them see some of the challenges of simplifying fractions that contain addition(or subtraction) and recognize that some mathematical tools (i.e. factoring!) can provide a useful alternative for overcoming these challenges.

Avoiding Common Misconceptions
Connection to Prior Knowledge: Avoiding Common Misconceptions

# Operations with Rational Expressions

Unit 5: Rational and Inverse Functions
Lesson 3 of 8

## Big Idea: Operations with rational expressions are just like operations with fractions.

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Standards:
Subject(s):
Math, rational exponents, Algebra, rational expressions, composite function, inverse functions, domain, range, arithmetic with rational expressions, rational function
90 minutes

### Colleen Werner

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