Note:

- A rational equation is an equation where at least one denominator
contains a variable.
- When a 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 is solving a rational equation is to convert the
equation to an equation without denominators. This new equation may be
equivalent (same solutions as the original equation) or it may not be
equivalent (extraneous solutions).
- The next step is to set the equation equal to zero and solve.
- Remember that you are trying to isolate the variable.
- Depending on the problem, there are several methods available to help you solve the problem.

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

**Solve for x in the following equation.**

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**Problem 5.5 b: ****
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**Answer: ****
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**Simplify the equation by subtracting **6

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**Multiply both sides of the equation by an expression that represents the
lowest common denominator. The expression **** is the
smallest expression because it is the smallest expression that is divisible
by all the denominators.**

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**The only way a product can equal zero is if at least one of the factors
equals zero.
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**Check the answer in the original equation.****
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**Check the solution ***x*=6** by substituting **6

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**Left Side:****
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**Right Side:****.**

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**Since the left side of the original equation is equal to the right side of
the original equation after we substitute the value **6

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**Check the solution ***x*=3.618** by substituting **3.618

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**Left Side:****
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**Right Side:****.**

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**Since the left side of the original equation is equal to the right side of
the original equation after we substitute the value **3.618

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**Check the solution ***x*=1.382** by substituting **1.382

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**Left Side:****
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**Right Side:****
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**Since the left side of the original equation is equal to the right side of
the original equation after we substitute the value **-1.236

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**You can also check your answer by graphing
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(formed by subtracting the right side of the original equation from the left side). Look to see where the graph crosses the x-axis; that will be the real solution. Note that the graph crosses the x-axis at three spots,

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

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If you would like to go back to the equation table of contents, click on
Contents**

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