# Solving Rational Equations

These lessons help Algebra and Grade 9 students learn how to solve rational equations.

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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

### 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(y2 - 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/(x2 - 4) + 1
4. 2/(x2 - x) = 1/(x - 1)
5. 3/(x + 2) = 6/(x - 1)

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