Calculus Examples

$\frac{lim_{x \to 1} 2 x}{x^{2} - 1}$

Step 1

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$\frac{2 lim_{x \to 1} x}{x^{2} - 1}$

Step 2

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$\frac{2 \cdot 1}{x^{2} - 1}$

Step 3

Simplify the answer.

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Step 3.1

Multiply $2$ by $1$ .

$\frac{2}{x^{2} - 1}$

Step 3.2

Simplify the denominator.

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Step 3.2.1

Rewrite $1$ as $1^{2}$ .

$\frac{2}{x^{2} - 1^{2}}$

Step 3.2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

$\frac{2}{(x + 1) (x - 1)}$