Solve for x e^x-e^(-x)=0

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

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

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

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

$x = - x$

Solve for $x$ .

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

Add $x$ to both sides of the equation.

$x + x = 0$

Add $x$ and $x$ .

$2 x = 0$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $0$ by $2$ .

$x = 0$