Solve 3+1/m-20/n=0

$$3 + \frac { 1 } { m } - \frac { 20 } { n } = 0$$

Solve for m

$$m=-\frac{n}{3n-20}$$

$$n\neq 0\text{ and }n\neq \frac{20}{3}$$

Steps for Solving Linear Equation

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

$$mn\times 3+n-m\times 20=0$$

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

$$mn\times 3-m\times 20=-n$$

Multiply -1 and 20 to get -20.

$$mn\times 3-20m=-n$$

Combine all terms containing m.

$$\left(n\times 3-20\right)m=-n$$

The equation is in standard form.

$$\left(3n-20\right)m=-n$$

Divide both sides by -20+3n.

$$\frac{\left(3n-20\right)m}{3n-20}=-\frac{n}{3n-20}$$

Dividing by -20+3n undoes the multiplication by -20+3n.

$$m=-\frac{n}{3n-20}$$

Variable m cannot be equal to 0.

$$m=-\frac{n}{3n-20}\text{, }m\neq 0$$

Solve for n

$$n=\frac{20m}{3m+1}$$

$$m\neq 0\text{ and }m\neq -\frac{1}{3}$$

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 mn, the least common multiple of m,n.

$$mn\times 3+n-m\times 20=0$$

Add m\times 20 to both sides. Anything plus zero gives itself.

$$mn\times 3+n=m\times 20$$

Combine all terms containing n.

$$\left(m\times 3+1\right)n=m\times 20$$

The equation is in standard form.

$$\left(3m+1\right)n=20m$$

Divide both sides by 3m+1.

$$\frac{\left(3m+1\right)n}{3m+1}=\frac{20m}{3m+1}$$

Dividing by 3m+1 undoes the multiplication by 3m+1.

$$n=\frac{20m}{3m+1}$$

Variable n cannot be equal to 0.

$$n=\frac{20m}{3m+1}\text{, }n\neq 0$$