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

Math
Take the limit of each term.
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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 limits by plugging in for all occurrences of .
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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 .
Simplify the answer.
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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)

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