Solve operatorname{nh}x=e^x-e^-x/2

$$\operatorname { nh } x = \frac { e ^ { x } - e ^ { - x } } { 2 }$$

Solve for h

$$\left\{\begin{matrix}h=-\frac{1-e^{2x}}{2nxe^{x}}\text{, }&x\neq 0\text{ and }n\neq 0\\h\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2nhx=e^{x}-e^{-x}$$

The equation is in standard form.

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

Divide both sides by 2nx.

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

Dividing by 2nx undoes the multiplication by 2nx.

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

Divide e^{x}-\frac{1}{e^{x}} by 2nx.

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

Solve for n

$$\left\{\begin{matrix}n=-\frac{1-e^{2x}}{2hxe^{x}}\text{, }&x\neq 0\text{ and }h\neq 0\\n\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2nhx=e^{x}-e^{-x}$$

The equation is in standard form.

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

Divide both sides by 2hx.

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

Dividing by 2hx undoes the multiplication by 2hx.

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

Divide e^{x}-\frac{1}{e^{x}} by 2hx.

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