Solve 17-1/r+12/s=0

$$17 - \frac { 1 } { r } + \frac { 12 } { s } = 0$$

Solve for r

$$r=\frac{s}{17s+12}$$

$$s\neq 0\text{ and }s\neq -\frac{12}{17}$$

Steps for Solving Linear Equation

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

$$rs\times 17-s+r\times 12=0$$

Add s to both sides. Anything plus zero gives itself.

$$rs\times 17+r\times 12=s$$

Combine all terms containing r.

$$\left(s\times 17+12\right)r=s$$

The equation is in standard form.

$$\left(17s+12\right)r=s$$

Divide both sides by 12+17s.

$$\frac{\left(17s+12\right)r}{17s+12}=\frac{s}{17s+12}$$

Dividing by 12+17s undoes the multiplication by 12+17s.

$$r=\frac{s}{17s+12}$$

Variable r cannot be equal to 0.

$$r=\frac{s}{17s+12}\text{, }r\neq 0$$

Solve for s

$$s=-\frac{12r}{17r-1}$$

$$r\neq 0\text{ and }r\neq \frac{1}{17}$$

Steps for Solving Linear Equation

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

$$rs\times 17-s+r\times 12=0$$

Subtract r\times 12 from both sides. Anything subtracted from zero gives its negation.

$$rs\times 17-s=-r\times 12$$

Multiply -1 and 12 to get -12.

$$rs\times 17-s=-12r$$

Combine all terms containing s.

$$\left(r\times 17-1\right)s=-12r$$

The equation is in standard form.

$$\left(17r-1\right)s=-12r$$

Divide both sides by 17r-1.

$$\frac{\left(17r-1\right)s}{17r-1}=-\frac{12r}{17r-1}$$

Dividing by 17r-1 undoes the multiplication by 17r-1.

$$s=-\frac{12r}{17r-1}$$

Variable s cannot be equal to 0.

$$s=-\frac{12r}{17r-1}\text{, }s\neq 0$$