Calculus Examples

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

Step 1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $- 8$ .

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

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 8$ .

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

Step 3

Evaluate the limit of $8$ which is constant as $x$ approaches $- 8$ .

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

Step 4

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 8$ .

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

Step 5

Evaluate the limit of $8$ which is constant as $x$ approaches $- 8$ .

$\frac{lim_{x \to - 8} x + 8}{lim_{x \to - 8} x - 1 \cdot 8}$

Step 6

Evaluate the limits by plugging in $- 8$ for all occurrences of $x$ .

Tap for more steps...

Step 6.1

Evaluate the limit of $x$ by plugging in $- 8$ for $x$ .

$\frac{- 8 + 8}{lim_{x \to - 8} x - 1 \cdot 8}$

Step 6.2

Evaluate the limit of $x$ by plugging in $- 8$ for $x$ .

$\frac{- 8 + 8}{- 8 - 1 \cdot 8}$

Step 7

Simplify the answer.

Tap for more steps...

Step 7.1

Cancel the common factor of $- 8 + 8$ and $- 8 - 1 \cdot 8$ .

Tap for more steps...

Step 7.1.1

Rewrite $- 8$ as $- 1 (8)$ .

$\frac{- 8 + 8}{- 1 (8) - 1 \cdot 8}$

Step 7.1.2

Factor $- 1$ out of $- 1 \cdot 8$ .

$\frac{- 8 + 8}{- 1 (8) - 1 (8)}$

Step 7.1.3

Factor $- 1$ out of $- 1 (8) - 1 (8)$ .

$\frac{- 8 + 8}{- 1 (8 + 8)}$

Step 7.1.4

Factor $8$ out of $- 8$ .

$\frac{8 \cdot - 1 + 8}{- 1 (8 + 8)}$

Step 7.1.5

Factor $8$ out of $8$ .

$\frac{8 \cdot - 1 + 8 \cdot 1}{- 1 (8 + 8)}$

Step 7.1.6

Factor $8$ out of $8 \cdot - 1 + 8 \cdot 1$ .

$\frac{8 \cdot (- 1 + 1)}{- 1 (8 + 8)}$

Step 7.1.7

Cancel the common factors.

Tap for more steps...

Step 7.1.7.1

Factor $8$ out of $- 1 (8 + 8)$ .

$\frac{8 \cdot (- 1 + 1)}{8 (- 1 (1 + 1))}$

Step 7.1.7.2

Cancel the common factor.

$\frac{8 \cdot (- 1 + 1)}{8 (- 1 (1 + 1))}$

Step 7.1.7.3

Rewrite the expression.

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

Step 7.2

Add $- 1$ and $1$ .

$\frac{0}{- 1 (1 + 1)}$

Step 7.3

Add $1$ and $1$ .

$\frac{0}{- 1 \cdot 2}$

Step 7.4

Multiply $- 1$ by $2$ .

$\frac{0}{- 2}$

Step 7.5

Divide $0$ by $- 2$ .

$0$