Solve c=f(1+1/m)

$$c = f ( 1 + \frac { 1 } { m } )$$

Solve for f

$$\left\{\begin{matrix}f=\frac{cm}{m+1}\text{, }&m\neq -1\text{ and }m\neq 0\\f\in \mathrm{R}\text{, }&m=-1\text{ and }c=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by m.

$$cm=f\left(1+\frac{1}{m}\right)m$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{m}{m}.

$$cm=f\left(\frac{m}{m}+\frac{1}{m}\right)m$$

Since \frac{m}{m} and \frac{1}{m} have the same denominator, add them by adding their numerators.

$$cm=f\times \frac{m+1}{m}m$$

Express f\times \frac{m+1}{m} as a single fraction.

$$cm=\frac{f\left(m+1\right)}{m}m$$

Express \frac{f\left(m+1\right)}{m}m as a single fraction.

$$cm=\frac{f\left(m+1\right)m}{m}$$

Cancel out m in both numerator and denominator.

$$cm=f\left(m+1\right)$$

Use the distributive property to multiply f by m+1.

$$cm=fm+f$$

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

$$fm+f=cm$$

Combine all terms containing f.

$$\left(m+1\right)f=cm$$

Divide both sides by m+1.

$$\frac{\left(m+1\right)f}{m+1}=\frac{cm}{m+1}$$

Dividing by m+1 undoes the multiplication by m+1.

$$f=\frac{cm}{m+1}$$

Solve for c

$$c=f+\frac{f}{m}$$

$$m\neq 0$$