Calculus Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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 $b = 1$ .

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

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 0$

Step 3