Split the limit using the Sum of Limits Rule on the limit as approaches .

Split the limit using the Limits Quotient Rule on the limit as approaches .

Move the limit under the radical sign.

Split the limit using the Sum of Limits Rule on the limit as approaches .

Move the limit under the radical sign.

Split the limit using the Sum of Limits Rule on the limit as approaches .

Split the limit using the Limits Quotient Rule on the limit as approaches .

Evaluate the limit of which is constant as approaches .

Evaluate the limit of by plugging in for .

Evaluate the limit of which is constant as approaches .

Evaluate the limit of by plugging in for .

Evaluate the limit of which is constant as approaches .

Evaluate the limit of which is constant as approaches .

Subtract from .

Simplify each term.

Combine and into a single radical.

Subtract from .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Rewrite as .

Any root of is .

Simplify the denominator.

Rewrite as .

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

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine the numerators over the common denominator.

Subtract from .

Divide by .

Evaluate limit as x approaches 8 of ( square root of 12-x)/( square root of 24-x)-2/4