Calculus Examples

$lim_{x \to 1} (\frac{x}{x - 1}) - (\frac{1}{x - 1})$

Step 1

Combine fractions using a common denominator.

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Step 1.1

Combine the numerators over the common denominator.

$lim_{x \to 1} \frac{x - 1}{x - 1}$

Step 1.2

Cancel the common factor of $x - 1$ .

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Step 1.2.1

Cancel the common factor.

$lim_{x \to 1} \frac{x - 1}{x - 1}$

Step 1.2.2

Rewrite the expression.

$lim_{x \to 1} 1$

Step 2

Evaluate the limit of $1$ which is constant as $x$ approaches $1$ .

$1$