Rational Expressions with Opposite Signs: How to Simplify

Do students understand how to simplify rational expressions with opposite signs? Keep reading to discover strategies for success.

#1 – Simplifying Fractions

First, introduce students to what they are familiar with. Start with what they know before adding new elements of greater complexity. Providing a review will decrease the number of times students ask questions related to basic fraction operations when solving rational expressions.

For example, I begin with a simple problem such as 5/10. See the examples below.

In addition, include a fraction that reduces to a number over 1.

#2 – Simplifying Fractions with Integers

Next, you are hoping that students remember integer rules. On the other hand, I include this concept just to be thorough.

Again, emphasize the equivalent value of each answer, regardless of the location of the negative sign. Students often forget this.

#3 – Rational Expressions Equivalent to One

Furthermore, remind students that a set of positive terms divided by the same set of positive terms is one, not zero. During review, emphasize this by using a simple illustration as given below.

For example, I notice this error with problems like the one below. When students slash through the top and bottom of the expression, they assume that the answer is zero. Emphasize the invisible 1 in front of each.