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 term outside of the limit because it is constant with respect to .

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 inside the logarithm.

Evaluate the limit of by plugging in for .

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 .

Evaluate the limit of by plugging in for .

Multiply by .

Subtract from .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Evaluate limit as x approaches 8 of (5x)/(x-1)-5/( natural log of x)