Solve 8=w/n_{1}+w/n_{2}

$$8 = \frac { w } { n _ { 1 } } + \frac { w } { n _ { 2 } }$$

Solve for n_1

$$n_{1}=-\frac{n_{2}w}{w-8n_{2}}$$

$$n_{2}\neq 0\text{ and }w\neq 0\text{ and }w\neq 8n_{2}$$

Steps for Solving Linear Equation

Variable n_{1} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by n_{1}n_{2}, the least common multiple of n_{1},n_{2}.

$$8n_{1}n_{2}=n_{2}w+n_{1}w$$

Subtract n_{1}w from both sides.

$$8n_{1}n_{2}-n_{1}w=n_{2}w$$

Combine all terms containing n_{1}.

$$\left(8n_{2}-w\right)n_{1}=n_{2}w$$

Divide both sides by 8n_{2}-w.

$$\frac{\left(8n_{2}-w\right)n_{1}}{8n_{2}-w}=\frac{n_{2}w}{8n_{2}-w}$$

Dividing by 8n_{2}-w undoes the multiplication by 8n_{2}-w.

$$n_{1}=\frac{n_{2}w}{8n_{2}-w}$$

Variable n_{1} cannot be equal to 0.

$$n_{1}=\frac{n_{2}w}{8n_{2}-w}\text{, }n_{1}\neq 0$$

Solve for n_2

$$n_{2}=-\frac{n_{1}w}{w-8n_{1}}$$

$$n_{1}\neq 0\text{ and }w\neq 0\text{ and }w\neq 8n_{1}$$

Steps for Solving Linear Equation

Variable n_{2} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by n_{1}n_{2}, the least common multiple of n_{1},n_{2}.

$$8n_{1}n_{2}=n_{2}w+n_{1}w$$

Subtract n_{2}w from both sides.

$$8n_{1}n_{2}-n_{2}w=n_{1}w$$

Combine all terms containing n_{2}.

$$\left(8n_{1}-w\right)n_{2}=n_{1}w$$

Divide both sides by 8n_{1}-w.

$$\frac{\left(8n_{1}-w\right)n_{2}}{8n_{1}-w}=\frac{n_{1}w}{8n_{1}-w}$$

Dividing by 8n_{1}-w undoes the multiplication by 8n_{1}-w.

$$n_{2}=\frac{n_{1}w}{8n_{1}-w}$$

Variable n_{2} cannot be equal to 0.

$$n_{2}=\frac{n_{1}w}{8n_{1}-w}\text{, }n_{2}\neq 0$$