Precalculus Examples

$\frac{lim_{x \to - 2} x - 2}{x^{2} - 4}$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 2$ .

$\frac{lim_{x \to - 2} x - lim_{x \to - 2} 2}{x^{2} - 4}$

Step 1.2

Evaluate the limit of $2$ which is constant as $x$ approaches $- 2$ .

$\frac{lim_{x \to - 2} x - 1 \cdot 2}{x^{2} - 4}$

Step 2

Evaluate the limit of $x$ by plugging in $- 2$ for $x$ .

$\frac{- 2 - 1 \cdot 2}{x^{2} - 4}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Simplify the numerator.

Tap for more steps...

Step 3.1.1

Multiply $- 1$ by $2$ .

$\frac{- 2 - 2}{x^{2} - 4}$

Step 3.1.2

Subtract $2$ from $- 2$ .

$\frac{- 4}{x^{2} - 4}$

Step 3.2

Simplify the denominator.

Tap for more steps...

Step 3.2.1

Rewrite $4$ as $2^{2}$ .

$\frac{- 4}{x^{2} - 2^{2}}$

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 $b = 2$ .

$\frac{- 4}{(x + 2) (x - 2)}$

Step 3.3

Move the negative in front of the fraction.

$- \frac{4}{(x + 2) (x - 2)}$