Students often report that working with fractions is difficult because there are special rules for learning how to add, subtract, multiply, and divide them. However, once these operations with fractions are understood, we can find that working with fractions is not so challenging after all.
Rational expressions are like fractions, in that they are written as the quotient of two expressions (like a fraction) and require similar processes for simplifying and solving them as fractions do. So like fractions, students may first consider rational expressions to be difficult to simplify or rational expression difficult to solve, but if we master our understanding of how to work with fractions, we can apply those same principles to rational expressions.
In the end, what we'll find in this unit is that learning how to solve rational equations is a critical element in Algebra 1, because many applications require us to express a problem mathematically using variables in either the numerator or denominator of a rational expression. This makes learning how to solve rational equations a important tool in our mathematical tool belts.
Guiding Questions for Unit 6:
How do processes for performing operations with fractions relate to operations with rational expressions?
How do processes for solving equations containing fractions relate to solving rational equations?
How can rational equations be used to solve application problems?
Lessons in Unit 6:
Lesson 1: Simplifying Rational Expressions
Lesson 2: Multiplying and Dividing Rational Expressions
Lesson 3: Adding and Subtracting Rational Expressions (with like denominators)
Lesson 4: Adding and Subtracting Rational Expressions (with unlike denominators)