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

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

Use the quadratic formula to find the solutions.

Substitute the values , , and into the quadratic formula and solve for .

Simplify.

Simplify the numerator.

Raise to the power of .

Multiply by .

Multiply by .

Subtract from .

Rewrite as .

Rewrite as .

Rewrite as .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

Move to the left of .

Multiply by .

Simplify the expression to solve for the portion of the .

Simplify the numerator.

Raise to the power of .

Multiply by .

Multiply by .

Subtract from .

Rewrite as .

Rewrite as .

Rewrite as .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

Move to the left of .

Multiply by .

Change the to .

Simplify the expression to solve for the portion of the .

Simplify the numerator.

Raise to the power of .

Multiply by .

Multiply by .

Subtract from .

Rewrite as .

Rewrite as .

Rewrite as .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

Move to the left of .

Multiply by .

Change the to .

The final answer is the combination of both solutions.

The domain is all real numbers.

Interval Notation:

Set-Builder Notation:

The range is the set of all valid values. Use the graph to find the range.

Interval Notation:

Set-Builder Notation:

Determine the domain and range.

Domain:

Range:

Find the Domain and Range f(x)=(5x^2-9x-9)/(8x^2-2x+8)