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More Lessons for Grade 9 Math

Math Worksheets

Examples, solutions, videos, and worksheets to help Algebra and Grade 9 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.

**Solve rational equations, basics**

Step 1: Multiply by LCD

Step 2: Solve resulting equation

Step 3: Check solution. Reject any solution that makes the denominator = 0

Examples:

Solve and check the answer:

19y/6 - 5y/2 = 4

b/5 - (b - 1)/10 = 9/10**Solving Rational Equations**

Examples:

6/x^{2} - 5/x = 1

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

1/(x + 3) + 1/(x - 3) = 6(x^{2} - 9)

**Rational Equations - Algebra Help**

Students learn that when solving 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, and solve from here.

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:

5/(y + 2) = 13(y^{2} - 3y - 10) + (-3)/(y - 5)
**Solving Rational Equations**

Examples:

Solve the following equations, check for extraneous solutions.

1. 4/x + 5/2 = -11/x

2. 5x/(x - 2) = 7 + 10/(x - 2)

3. (3x - 2)/(x - 2) = 6/(x^{2} - 4) + 1

4. 2/(x^{2} - x) = 1/(x - 1)

5. 3/(x + 2) = 6/(x - 1)

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.

Step 1: Multiply by LCD

Step 2: Solve resulting equation

Step 3: Check solution. Reject any solution that makes the denominator = 0

Examples:

Solve and check the answer:

19y/6 - 5y/2 = 4

b/5 - (b - 1)/10 = 9/10

Examples:

6/x

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

1/(x + 3) + 1/(x - 3) = 6(x

Students learn that when solving 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, and solve from here.

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:

5/(y + 2) = 13(y

Examples:

Solve the following equations, check for extraneous solutions.

1. 4/x + 5/2 = -11/x

2. 5x/(x - 2) = 7 + 10/(x - 2)

3. (3x - 2)/(x - 2) = 6/(x

4. 2/(x

5. 3/(x + 2) = 6/(x - 1)

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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