Calculus Examples

$\frac{10 e^{2 x} - 10}{e^{x} - 1}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Factor $10$ out of $10 e^{2 x} - 10$ .

Tap for more steps...

Step 1.1.1

Factor $10$ out of $10 e^{2 x}$ .

$\frac{10 (e^{2 x}) - 10}{e^{x} - 1}$

Step 1.1.2

Factor $10$ out of $- 10$ .

$\frac{10 (e^{2 x}) + 10 (- 1)}{e^{x} - 1}$

Step 1.1.3

Factor $10$ out of $10 (e^{2 x}) + 10 (- 1)$ .

$\frac{10 (e^{2 x} - 1)}{e^{x} - 1}$

Step 1.2

Rewrite $e^{2 x}$ as ${(e^{x})}^{2}$ .

$\frac{10 ({(e^{x})}^{2} - 1)}{e^{x} - 1}$

Step 1.3

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

$\frac{10 ({(e^{x})}^{2} - 1^{2})}{e^{x} - 1}$

Step 1.4

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

$\frac{10 (e^{x} + 1) (e^{x} - 1)}{e^{x} - 1}$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Cancel the common factor of $e^{x} - 1$ .

Tap for more steps...

Step 2.1.1

Cancel the common factor.

$\frac{10 (e^{x} + 1) (e^{x} - 1)}{e^{x} - 1}$

Step 2.1.2

Divide $10 (e^{x} + 1)$ by $1$ .

$10 (e^{x} + 1)$

Step 2.2

Apply the distributive property.

$10 e^{x} + 10 \cdot 1$

Step 2.3

Multiply $10$ by $1$ .

$10 e^{x} + 10$