# Rewriting Rational Expressions Worksheets

The name rational expression indicates exact what they are. They are a ration between two polynomials. They are rationale since one is being divided by the other. There will be many times that we come across these types of expressions, and we get stuck, but you must remember that you can always rewrite expressions to suit your needs and primarily to make the math work for you. Students can use these worksheets and lesson to understand how rewrite fraction in which the numerator and/or the denominator are polynomials.

### Aligned Standard: HSA-APR.D.6

- Simplifying Complex Expressions Step-by-step Lesson- This start out looking a bit intimidating, but it progresses to a manageable problem very quickly.
- Guided Lesson - Always remember to get everything into the simplest format.
- Guided Lesson Explanation - We get you in the habit of canceling and simplifying.
- Practice Worksheet - These are mostly quotient based. The reason behind that is that operation appears nine out of ten times on the last ten major AP Algebra examines. The other operations are often neglected.
- Matching Worksheet - Match the expression to its simplified form.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

It's all about understanding what the reciprocal process entails. Examples are worked out for you.

- Homework 1 - This example shows you how to factor out the GCF of the denominator, in this case g.
- Homework 2 - Cancel the common or like factors. You will find that we really liked the variable (x) here.
- Homework 3 - We are in the simplest form. Put what you learned into practice.

### Practice Worksheets

It might be a good idea to review factoring before progressing on to these.

- Practice 1 - Simplify these problems to provide you practice in moving things around and apart.
- Practice 2 - It is all about identifying the like terms.
- Practice 3 - Simplify the rational expression by rewriting them using all the elements. Remember to accomodate all the terms.

### Math Skill Quizzes

The first quiz focuses on integers, the second focuses on variables, and the third is a mixed bag.

- Quiz 1 - Plenty of space to stretch out your writing.
- Quiz 2 - Larger values for you to deal here with.
- Quiz 3 - If you can find a whole number that fits all, you are golden.

### How to Rewrite Rational Expressions

We have to start back with realizing that these types of expressions are fractions. The only difference between these fractions and those we are accustomed to working with is that both the numerator and denominators are polynomials. Polynomials can be complicated to work with because they often contain unknown values called variables. This is a pretty complicated equation to solve, given that there are several expressions that are different from each other. It is even more difficult if you can't recognize the common factors that exist between the numerator and denominator. But, if you follow a basic strategy and work flow it is not as problematic as you might first think.

Start by identifying the set of all possible variables (domain) for the variable. Since the denominator cannot be equal to zero (ever), we can determine all the possible values of the variable that would make the denominator zero. Those are called the excluded values, meaning they cannot happen, man! So, we throw those out from the get-go.

Once we know the excluded values, it is time to get our simplify on. Always look for common factors that exist both in the numerator and denominator. Remember that you can also rewrite a numeric value into factors, if that helps. For example, 16 can be rewritten as (4 x 4). Keep working on this until you are sure everything is in the lowest terms possible.

For example, evaluate and ultimately rewrite: (6x^{2} + 18x + 15) / x + 3

Let's look at an example: 529/23

Now, if we consider the above equation as a division between the two, we can understand that:

529/23 = 23/1 = 23

Using the process of long division, we can easily rewrite the equation mentioned above.

(6x^{2} + 18x + 15) / x + 3

Rewritten from: (x + 15) / 1.