Solve fx=5/2left(e^cx+e^-cxright)

$$fx= \frac{ 5 }{ 2 } \left( { e }^{ cx } + { e }^{ -cx } \right)$$

Solve for f

$$f=\frac{5\left(e^{2cx}+1\right)}{2xe^{cx}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{5}{2} by e^{cx}+e^{\left(-c\right)x}.

$$fx=\frac{5}{2}e^{cx}+\frac{5}{2}e^{\left(-c\right)x}$$

Reorder the terms.

$$fx=\frac{5}{2}e^{cx}+\frac{5}{2}e^{-cx}$$

The equation is in standard form.

$$xf=\frac{5}{2e^{cx}}+\frac{5e^{cx}}{2}$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{\frac{5}{2e^{cx}}+\frac{5e^{cx}}{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{\frac{5}{2e^{cx}}+\frac{5e^{cx}}{2}}{x}$$

Divide \frac{5e^{cx}}{2}+\frac{5}{2e^{cx}} by x.

$$f=\frac{5\left(e^{2cx}+1\right)}{2xe^{cx}}$$