Solve C=b(1+1/m)

$$C = b ( 1 + \frac { 1 } { m } )$$

Solve for b

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

Steps for Solving Linear Equation

Multiply both sides of the equation by m.

$$Cm=b\left(1+\frac{1}{m}\right)m$$

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

$$Cm=b\left(\frac{m}{m}+\frac{1}{m}\right)m$$

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

$$Cm=b\times \frac{m+1}{m}m$$

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

$$Cm=\frac{b\left(m+1\right)}{m}m$$

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

$$Cm=\frac{b\left(m+1\right)m}{m}$$

Cancel out m in both numerator and denominator.

$$Cm=b\left(m+1\right)$$

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

$$Cm=bm+b$$

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

$$bm+b=Cm$$

Combine all terms containing b.

$$\left(m+1\right)b=Cm$$

Divide both sides by m+1.

$$\frac{\left(m+1\right)b}{m+1}=\frac{Cm}{m+1}$$

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

$$b=\frac{Cm}{m+1}$$

Solve for C

$$C=b+\frac{b}{m}$$

$$m\neq 0$$