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Examples, Solutions, videos, worksheets, and activities to help Algebra students learn how to solve rational equations.

The following figure shows how to solve rational equations. Scroll down the page for more examples and solutions.

**Solving Rational Equations**

In a rational equation, there will be a variable in the denominator of a fraction. Use cross multiplying when solving rational equations.

Examples:

3/(2x + 1) = 5

2/x - 3/(x + 1) = 9

**Advanced Rational Equations - Algebra Help**

Students learn that when solving advanced rational equations, the first step is to factor each of the denominators, if possible, then multiply both sides of the equation by the common denominator for all the fractions in order to get rid of the fractions.

Note that in this lesson, once the fractions have been removed from the equation, the result will be a polynomial equation, so remember the rules for solving polynomial equations: set the equation equal to zero, then factor.

Finally, check each solution to see if it makes a denominator in the original equation equal to zero. If so, then it cannot be a solution to the equation.

Example:

(x - 2)/4 + 1 = 12/x

**Solving Rational Equations**

5/(3x - 4) = 2/(x + 1)

-x/(x - 2) + (3x - 1)/(x + 4) = 1/(x^{2} + 2x - 8)
**Two more examples of solving rational equations**

x + 1/x = 2

2/(x^{2} + 4x + 3) = 2 + (x -2)/(x + 3)

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Grade 9 Math

Math Worksheets

The following figure shows how to solve rational equations. Scroll down the page for more examples and solutions.

In a rational equation, there will be a variable in the denominator of a fraction. Use cross multiplying when solving rational equations.

Examples:

3/(2x + 1) = 5

2/x - 3/(x + 1) = 9

Students learn that when solving advanced rational equations, the first step is to factor each of the denominators, if possible, then multiply both sides of the equation by the common denominator for all the fractions in order to get rid of the fractions.

Note that in this lesson, once the fractions have been removed from the equation, the result will be a polynomial equation, so remember the rules for solving polynomial equations: set the equation equal to zero, then factor.

Finally, check each solution to see if it makes a denominator in the original equation equal to zero. If so, then it cannot be a solution to the equation.

Example:

(x - 2)/4 + 1 = 12/x

5/(3x - 4) = 2/(x + 1)

-x/(x - 2) + (3x - 1)/(x + 4) = 1/(x

x + 1/x = 2

2/(x

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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