Solve 3z/m+n/b=f

$$\frac { 3 z } { m } + \frac { n } { b } = f$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{mn}{3z-fm}\text{, }&m\neq 0\text{ and }n\neq 0\text{ and }z\neq \frac{fm}{3}\\b\neq 0\text{, }&z=\frac{fm}{3}\text{ and }n=0\text{ and }m\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by bm, the least common multiple of m,b.

$$b\times 3z+mn=fbm$$

Subtract fbm from both sides.

$$b\times 3z+mn-fbm=0$$

Subtract mn from both sides. Anything subtracted from zero gives its negation.

$$b\times 3z-fbm=-mn$$

Combine all terms containing b.

$$\left(3z-fm\right)b=-mn$$

Divide both sides by 3z-mf.

$$\frac{\left(3z-fm\right)b}{3z-fm}=-\frac{mn}{3z-fm}$$

Dividing by 3z-mf undoes the multiplication by 3z-mf.

$$b=-\frac{mn}{3z-fm}$$

Variable b cannot be equal to 0.

$$b=-\frac{mn}{3z-fm}\text{, }b\neq 0$$

Solve for f

$$f=\frac{3bz+mn}{bm}$$

$$m\neq 0\text{ and }b\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by bm, the least common multiple of m,b.

$$b\times 3z+mn=fbm$$

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

$$fbm=b\times 3z+mn$$

The equation is in standard form.

$$bmf=3bz+mn$$

Divide both sides by bm.

$$\frac{bmf}{bm}=\frac{3bz+mn}{bm}$$

Dividing by bm undoes the multiplication by bm.

$$f=\frac{3bz+mn}{bm}$$

Divide 3zb+nm by bm.

$$f=\frac{n}{b}+\frac{3z}{m}$$