## How to Use a Rational Equation to Solve a Word Problem:

Use the procedures below to resolve a word issue when it contains a rational equation.

- Write the equation that the word problem suggests in step one. Pay attention to words that indicate equalities or mathematical procedures.
- Eliminate the fractional equation.
- Find the answer to the equation’s unknown.

## How to Use Rational Equations to Solve a Word Problem

We ought to be experts at solving word problems by this point in the course. Rational equations will frequently be used in practical situations. Let’s start by going over the six steps we use to solve word problems.

### Rational Expressions Word Problems: A Six-Step Approach

- Determine the information you are required to find by carefully reading the problem.
- Create a variable to stand in for the unknowable
- Create an equation that accurately reflects the current circumstance.
- Fix the problem.
- Give a decent, concise sentence as your response.
- Read the issue again to verify the outcome.

### Terminology for Rational Equations:

rational formula A fractional equation using polynomials is referred to as a rational equation.

Contents

- 1 How to Use a Rational Equation to Solve a Word Problem:
- 2 How to Use Rational Equations to Solve a Word Problem
- 3 How can rational equations be solved?
- 4 How Are Rational Equations Solved?
- 5 Extraneous Solutions and Excluded Values
- 6 Additional Logic Equations
- 7 A Rational Equation is what?
- 8 Reasonable Expression and Reasonable Equation
- 9 Images of Rational Equations Word Problems Worksheet
- 10 Download Rational Equations Word Problems Worksheet
- 11 Rational Equation Solving Techniques
- 12 Related posts of "Rational Equations Word Problems Worksheet"

A polynomial is an expression comprising several terms, each with a variable in a unique order (i.e. having a different exponent).

The two exercises that follow show you how to use a rational equation to solve a word problem.

## How can rational equations be solved?

This tutorial offers wonderful examples of how math is used in everyday life. This article demonstrates how to create a rational equation using the data from a word problem. After that, you’ll see how to resolve the equation and discover the solution!

One area of mathematics called algebra is concerned with the symbols and arithmetic operations connected to those symbols. This area of mathematics has a rather broad curriculum all by itself. Say one needs to break algebra out into several parts. There are numerous subsections in that scenario, including those on polynomials, linear equations in one variable, linear equations in two variables, quadratic equations, arithmetic progressions, rational expressions, exponents, and many others.

One of the key components of Elementary Algebra is the use of rational expressions. It is among the most significant areas of mathematics. Have you heard of rational equations? No! If so, this post is written just for you.

You will discover more about rational equations and phrases associated with them in this post.

## How Are Rational Equations Solved?

Obtaining the values of the variables included in a rational equation is a requirement for solving a rational equation. The issue of how to resolve rational equations now arises. When solving rational equations, the fractions are cleared by multiplying both sides of the equation by the denominator’s least common multiple. Do not forget that the denominator shouldn’t be 0.

Rational equations can be solved using a variety of techniques. Factorization, the LCD method, LCM-based solutions, cross-multiplication, etc. are all examples of solutions. These days, calculators that solve rational equations are also employed to answer the given rational equations.

Calculators for solving rational equations can be found online and are used to determine the answer to a given variable in a rational equation.

We could have used fractions and sought a common denominator, but it frequently results in more errors. The same concept can be used to resolve rational equations. A rational equation can have polynomials in both the numerator and denominator of the fractions, which is how it differs from a linear equation. As a result, multiplying the entire rational equation by a polynomial may occasionally be required to clear the denominator. The denominators of a rational equation with a term that has a polynomial in the numerator will be removed in the following example.

We demonstrate how to solve a rational equation with a binomial in the denominator of one term in the following two examples. To remove the denominators from both fractions, we shall use the common denominator. Because there are no common factors between the denominators, the LCD is the product of both.

## Extraneous Solutions and Excluded Values

The denominator of some rational formulations contains a variable. There is an additional stage in solving them when this is the case. You must rule out values of the variable that would result in a denominator of 0 since division by 0 is undefinable. They are known as excluded values. Let’s examine a case in point.

You now know that there are multiple approaches to solving rational equations. Both of these methods can occasionally result in answers that don’t hold true when the equation is written in its original form since they modify and rearrange terms. Extraneous solutions are the name given to these types of solutions. Due to the possibility that some solutions to the original equations produce undefined expressions or yield false claims, it is always vital to double-check all of the answers.

## Additional Logic Equations

A quadratic can emerge from the solution of a rational equation occasionally. When this occurs, we continue the solution by using one of the techniques we have learned to simplify the quadratic equation. It might turn out there isn’t a solution at all.

## A Rational Equation is what?

An equation that provides an analogous relationship between two expressions and has one or more terms that are rational expressions is known as a rational equation. According to the definition of a rational equation, a rational equation has two sides and rational expression terms on both sides.

## Reasonable Expression and Reasonable Equation

One must pay close attention to the expression’s formatting in order to distinguish the rational equation from the rational expression. It is a rational expression if there isn’t an equals sign between the expressions. Otherwise, it is a rational equation, as was already mentioned.

## Images of Rational Equations Word Problems Worksheet

## Download Rational Equations Word Problems Worksheet

Download Rational Equations Word Problems Worksheet: **Click Here**

## Rational Equation Solving Techniques

### To solve rational equations, follow these steps:

- Find the equation’s excluded values. The values of the variable for which the denominator is zero are removed from the equation.
- By looking at the denominator and solving for zero, these are discovered.
- Finding the excluded values early aids in the subsequent detection of erroneous solutions.
- Analyze the numerators. If the denominators of the rational expressions disagree, get the LCM of the denominators.
- If all rational terms share the same denominator, multiply each term in the equation by either the denominator or the LCM of the denominator.
- After completing this step, there will only be a linear or a quadratic equation that needs to be solved.
- Use the quadratic equation-solving methods or the equality properties to solve the resulting problem.
- Look for unnecessary solutions. However, if any of the answers matched the excluded values on step 1, then that value cannot be a solution to the equation. Generally speaking, several of these values will make the equation true (even if it was found by normal means).