These worksheets will teach your students how to solve for variables in rational algebraic equations.

Rational equations contain at least one fraction. The fraction in these types of equations contain a polynomial either in the numerator or denominator. This section of our worksheets will walk you through this skill by taking baby steps towards making you completely independent with this. Make sure you deeply understand the guided lessons before you run off on your own with this. Use these rational equation worksheets to teach your students how to solve various problems dealing with rational equations and the variables that are found within them.

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Rational Equations Lesson

Rational Equations Lesson

Learn about how to process these types of rational equations by solving the following: (x+2)/6 = (2x-5)/5. You will then have 2 problems of your own to work on.

Worksheet 1

Worksheet 1

Solve these 10 rational equations. They make for really good practice. Here is an example of the types of problems on the worksheet: 1/(z+2) = 4/(z-6)

Worksheet 2

Worksheet 2

This is a slightly more advanced types of worksheet. The exponents start showing up in droves here. Example: (b2 - 4)/(b+2) = 1/(b+2)

Review Sheets

Review Sheets

Follow the steps to solve this equation: (x+5)/4 = (3x-7)/2. You will have 6 practice problems included with this one.

Rational Equations Quiz

Rational Equations Quiz

Solve the following problems dealing with radical equations, then check and score your answers. Example: 3x/(x2-16)+4/(x+4) = 2/(x-4)

Do Now Worksheet

Do Now

Complete these 3 problems as a class to see where anyone is having difficulty. This is an example problem: 3/(z+2) = 5/(z-2)

How to Solve Rational Equations?

A rational equation is a math equation in which one or more variables are fractions. To identify a rational equation, look for any fractions in the equation. All equations with fractions are considered to be rational equations.

For example, the equation 2x + 3 = 5 is not a rational equation because there are no fractions present. However, the equation 2x + 3 = 5/2 is rational because it has a fraction on one side of the equal sign. Even if it is a mixed number, as long as it has a numerator and a denominator, it fits the mold.

How Do You Solve A Rational Equation?

To solve these types of problems, you must first reduce all fractions to their simplest form. You will need to use the least common denominator (LCD). The LCD is the smallest number that all of the denominators in the equation will go into evenly.

Once you have ruled out the denominator, solving the equation is easier. The equation now is a simple algebraic equation that can be solved using the standard methods of solving algebraic equations.

It is important to note that when solving a rational equation, you must always check your answer by plugging it back into the original equation. This is how you will know if you have found the correct solution.

You might find the fractional parts concentrated on one side or on both sides. The most common way to solve these types of problems is to reduce the fractions to a common denominator and then solve for the numerators, but this doesn’t fit all problem types. The more complex equations contain variables on both sides of the equation. At first the denominators we require very little from you, as you advance these problems can require six or seven steps. A good process of solving these include converting everything to a common denominator and then multiplying by the common denominator to make them whole values. You will complete this process by cross multiplying. When students first see this, I would highly encourage them to write what they are doing in each step and some what create a math graphic organizer for themself. Some of the variables that you will find in these rational algebraic equations are not your everyday symbol. Students will apply basic algebraic properties such as cross multiplication in order to balance the equations. You'll also notice on a few of the worksheets that we throw in a little integer operational mathematics. This is purely to keep your students on their toes and make them actual step back and think about what they are doing.

Tips for Solving Rational Equations

Here are a few tips:

Make sure to reduce all fractions to their simplest form before attempting to solve the equation. This will make the equation easier to work with and help you avoid any mistakes.

Be careful when multiplying by the LCD, as you may accidentally introduce new solutions not previously present in the equation. If this happens, go back and check your work to make sure everything is correct.

Once you have simplified both sides of the equation, solve for x like you would with any other math equation. If you follow these steps, you should be able to solve any rational equation without too much trouble.

How to Reduce Fractions to Their Simplest Form?

You need to take a few steps to reduce fractions to their simplest form. First, find the greatest common factor (GCF) of the numerator and denominator. The GCF is the largest number that can be divided by both the numerator and denominator evenly.

Next, divide both the numerator and denominator by the GCF. This will give you a reduced fraction.

For example, let's say we have the fraction 4/6. The first step is to find the GCF of 4 and 6, which is 2. We then divide both the numerator and denominator by 2, giving us the reduced fraction of 2/3.

It's important to reduce fractions to their simplest form before attempting to solve a rational equation. This is because if you don't, you may accidentally introduce new solutions not previously present in the equation.