Solve fx=a/2cleft(e^cx+e^-cxright)

$$fx= \frac{ a }{ 2c } \left( { e }^{ cx } + { e }^{ -cx } \right)$$

Solve for a

$$a=\frac{2cfxe^{cx}}{e^{2cx}+1}$$

$$c\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2c.

$$fx\times 2c=a\left(e^{cx}+e^{\left(-c\right)x}\right)$$

Use the distributive property to multiply a by e^{cx}+e^{\left(-c\right)x}.

$$fx\times 2c=ae^{cx}+ae^{\left(-c\right)x}$$

Swap sides so that all variable terms are on the left hand side.

$$ae^{cx}+ae^{\left(-c\right)x}=fx\times 2c$$

Reorder the terms.

$$ae^{cx}+ae^{-cx}=2cfx$$

Combine all terms containing a.

$$\left(e^{cx}+e^{-cx}\right)a=2cfx$$

The equation is in standard form.

$$\left(\frac{1}{e^{cx}}+e^{cx}\right)a=2cfx$$

Divide both sides by e^{cx}+e^{-cx}.

$$\frac{\left(\frac{1}{e^{cx}}+e^{cx}\right)a}{\frac{1}{e^{cx}}+e^{cx}}=\frac{2cfx}{\frac{1}{e^{cx}}+e^{cx}}$$

Dividing by e^{cx}+e^{-cx} undoes the multiplication by e^{cx}+e^{-cx}.

$$a=\frac{2cfx}{\frac{1}{e^{cx}}+e^{cx}}$$

Divide 2cfx by e^{cx}+e^{-cx}.

$$a=\frac{2cfxe^{cx}}{e^{2cx}+1}$$