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

Add and .

Add to both sides of the equation.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

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

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.

Set the equal to .

Add to both sides of the equation.

Subtract from both sides of the equation.

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 .

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .

Set the first factor equal to and solve.

Set the first factor equal to .

Set the equal to .

Add to both sides of the equation.

Set the next factor equal to and solve.

Set the next factor equal to .

Subtract from both sides of the equation.

The final solution is all the values that make true.

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 less 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 not 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 less 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 not 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 not less than the right side , which means that the given statement is false.

False

False

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

True

False

True

False

False

True

False

True

False

False

The solution consists of all of the true intervals.

or

The result can be shown in multiple forms.

Inequality Form:

Interval Notation:

Solve for x (2x^2-7+3)/((x-2)^2(x+1))<0