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

**Related Pages**

Solving Equations

Simplifying Rational Expressions

Algebraic Expressions

More Algebra Lessons

Grade 9 Math Lessons

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

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)

**Examples:**

Solve the following equations, check for extraneous solutions.

- 4/x + 5/2 = -11/x
- 5x/(x - 2) = 7 + 10/(x - 2)
- (3x - 2)/(x - 2) = 6/(x
^{2}- 4) + 1 - 2/(x
^{2}- x) = 1/(x - 1) - 3/(x + 2) = 6/(x - 1)

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