Solve 1/n+4/p=5/m

$$\frac { 1 } { n } + \frac { 4 } { p } = \frac { 5 } { m }$$

Solve for m

$$m=\frac{5np}{4n+p}$$

$$n\neq 0\text{ and }p\neq 0\text{ and }n\neq -\frac{p}{4}$$

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 mnp, the least common multiple of n,p,m.

$$mp+mn\times 4=np\times 5$$

Reorder the terms.

$$4mn+mp=5np$$

Combine all terms containing m.

$$\left(4n+p\right)m=5np$$

Divide both sides by p+4n.

$$\frac{\left(4n+p\right)m}{4n+p}=\frac{5np}{4n+p}$$

Dividing by p+4n undoes the multiplication by p+4n.

$$m=\frac{5np}{4n+p}$$

Variable m cannot be equal to 0.

$$m=\frac{5np}{4n+p}\text{, }m\neq 0$$

Solve for n

$$n=-\frac{mp}{4m-5p}$$

$$p\neq 0\text{ and }m\neq 0\text{ and }p\neq \frac{4m}{5}$$

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 mnp, the least common multiple of n,p,m.

$$mp+mn\times 4=np\times 5$$

Subtract np\times 5 from both sides.

$$mp+mn\times 4-np\times 5=0$$

Multiply -1 and 5 to get -5.

$$mp+mn\times 4-5np=0$$

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

$$mn\times 4-5np=-mp$$

Combine all terms containing n.

$$\left(m\times 4-5p\right)n=-mp$$

The equation is in standard form.

$$\left(4m-5p\right)n=-mp$$

Divide both sides by 4m-5p.

$$\frac{\left(4m-5p\right)n}{4m-5p}=-\frac{mp}{4m-5p}$$

Dividing by 4m-5p undoes the multiplication by 4m-5p.

$$n=-\frac{mp}{4m-5p}$$

Variable n cannot be equal to 0.

$$n=-\frac{mp}{4m-5p}\text{, }n\neq 0$$