Finite Math Examples

$g (x) = \frac{e^{x} - e^{- x}}{3}$

Step 1

Set $\frac{e^{x} - e^{- x}}{3}$ equal to $0$ .

$\frac{e^{x} - e^{- x}}{3} = 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Set the numerator equal to zero.

$e^{x} - e^{- x} = 0$

Step 2.2

Solve the equation for $x$ .

Tap for more steps...

Step 2.2.1

Move $- e^{- x}$ to the right side of the equation by adding it to both sides.

$e^{x} = e^{- x}$

Step 2.2.2

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x = - x$

Step 2.2.3

Solve for $x$ .

Tap for more steps...

Step 2.2.3.1

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 2.2.3.1.1

Add $x$ to both sides of the equation.

$x + x = 0$

Step 2.2.3.1.2

Add $x$ and $x$ .

$2 x = 0$

Step 2.2.3.2

Divide each term in $2 x = 0$ by $2$ and simplify.

Tap for more steps...

Step 2.2.3.2.1

Divide each term in $2 x = 0$ by $2$ .

$\frac{2 x}{2} = \frac{0}{2}$

Step 2.2.3.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.3.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.3.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{0}{2}$

Step 2.2.3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{2}$

Step 2.2.3.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.3.2.3.1

Divide $0$ by $2$ .

$x = 0$

Step 3