# How do you evaluate #( ( x / (x-1 ) - (1 / lnx ) )# as x approaches 1+?

Using L'Hospital's Rule:

Differentiate numerator and denominator.

Plugging in 1:

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To evaluate the expression ( ( x / (x-1 ) - (1 / lnx ) ) as x approaches 1+, we can substitute the value of x into the expression and simplify.

As x approaches 1 from the right side (1+), we substitute x = 1 into the expression:

( ( 1 / (1-1 ) - (1 / ln1 ) )

Simplifying further:

( ( 1 / 0 ) - (1 / 0 ) )

Since the denominator becomes zero, the expression is undefined as x approaches 1 from the right side (1+).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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