## EQUATIONS INVOLVING FRACTIONS (RATIONAL EQUATIONS)

Note:

• A rational equation is an equation where at least one denominator contains a variable.

• There is a restriction on the domain. The variable cannot take on any number that would cause any denominator to be zero.

• The first step in solving a rational equation is to convert the equation to an equivalent equation without denominators.

• Then set the equation equal to zero and solve.

• Remember that you are trying to isolate the variable.

If you would like an in-depth review of fractions, click on Fractions.

Solve for x in the following equation.

Example 4:

The only way that a fraction can have a value of zero is when the numerator of the fraction is zero.

The numerator equals zero when x-5=0. Therefore the answer is x=5.

You can check your answer by graphing the function f(x) = . You will note that the graph crosses the x-axis at 5. This verifies our solution that x=5.

If you would like to work another example, click on Example

If you would like to test yourself by working some problems similar to this example, click on Problem

[Algebra] [Trigonometry]
[Geometry] [Differential Equations]
[Calculus] [Complex Variables] [Matrix Algebra]

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Author: Nancy Marcus