Calculus Examples

$lim_{x \to - 4} \frac{2 x}{x + 4} + \frac{8}{x + 4}$

Step 1

Combine fractions using a common denominator.

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Step 1.1

Combine the numerators over the common denominator.

$lim_{x \to - 4} \frac{2 x + 8}{x + 4}$

Step 1.2

Factor $2$ out of $2 x + 8$ .

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Step 1.2.1

Factor $2$ out of $2 x$ .

$lim_{x \to - 4} \frac{2 (x) + 8}{x + 4}$

Step 1.2.2

Factor $2$ out of $8$ .

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

Step 1.2.3

Factor $2$ out of $2 x + 2 \cdot 4$ .

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

Step 1.3

Cancel the common factor of $x + 4$ .

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Step 1.3.1

Cancel the common factor.

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

Step 1.3.2

Divide $2$ by $1$ .

$lim_{x \to - 4} 2$

Step 2

Evaluate the limit of $2$ which is constant as $x$ approaches $- 4$ .

$2$