Find all the values where the expression switches from negative to positive by setting each factor equal to and solving.

Set the equal to .

Add to both sides of the equation.

Add to both sides of the equation.

Take the square root of both sides of the equation to eliminate the exponent on the left side.

Simplify the right side of the equation.

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the to find the first solution.

Next, use the negative value of the to find the second solution.

The complete solution is the result of both the positive and negative portions of the solution.

Solve for each factor to find the values where the absolute value expression goes from negative to positive.

Consolidate the solutions.

Set the denominator in equal to to find where the expression is undefined.

Solve for .

Add to both sides of the equation.

Take the square root of both sides of the equation to eliminate the exponent on the left side.

The complete solution is the result of both the positive and negative portions of the solution.

Simplify the right side of the equation.

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the to find the first solution.

Next, use the negative value of the to find the second solution.

The complete solution is the result of both the positive and negative portions of the solution.

The domain is all values of that make the expression defined.

Use each root to create test intervals.

Test a value on the interval to see if it makes the inequality true.

Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

The left side is greater than the right side , which means that the given statement is always true.

True

True

Test a value on the interval to see if it makes the inequality true.

Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

The left side is less than the right side , which means that the given statement is false.

False

False

Test a value on the interval to see if it makes the inequality true.

Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

The left side is greater than the right side , which means that the given statement is always true.

True

True

Test a value on the interval to see if it makes the inequality true.

Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

The left side is greater than the right side , which means that the given statement is always true.

True

True

Compare the intervals to determine which ones satisfy the original inequality.

True

False

True

True

True

False

True

True

The solution consists of all of the true intervals.

or or

Combine the intervals.

Convert the inequality to interval notation.

Convert to Interval Notation ((x-5)^2)/(x^2-9)>=0