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

Take the limit of each term.
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 limits by plugging in for all occurrences of .
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

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