Solve z+1/y=m/n

$$z + \frac { 1 } { y } = \frac { m } { n }$$

Solve for m

$$m=nz+\frac{n}{y}$$

$$y\neq 0\text{ and }n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by ny, the least common multiple of y,n.

$$nyz+n=ym$$

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

$$ym=nyz+n$$

Divide both sides by y.

$$\frac{ym}{y}=\frac{nyz+n}{y}$$

Dividing by y undoes the multiplication by y.

$$m=\frac{nyz+n}{y}$$

Divide nzy+n by y.

$$m=nz+\frac{n}{y}$$

Solve for n

$$\left\{\begin{matrix}n=\frac{my}{yz+1}\text{, }&m\neq 0\text{ and }y\neq 0\text{ and }z\neq -\frac{1}{y}\\n\neq 0\text{, }&z=-\frac{1}{y}\text{ and }y\neq 0\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$nyz+n=ym$$

Reorder the terms.

$$nyz+n=my$$

Combine all terms containing n.

$$\left(yz+1\right)n=my$$

Divide both sides by zy+1.

$$\frac{\left(yz+1\right)n}{yz+1}=\frac{my}{yz+1}$$

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

$$n=\frac{my}{yz+1}$$

Variable n cannot be equal to 0.

$$n=\frac{my}{yz+1}\text{, }n\neq 0$$