Solve 1/r+1/q=1

$$\frac { 1 } { r } + \frac { 1 } { q } = 1$$

Solve for q

$$q=-\frac{r}{1-r}$$

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

Steps for Solving Linear Equation

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

$$q+r=qr$$

Subtract qr from both sides.

$$q+r-qr=0$$

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

$$q-qr=-r$$

Combine all terms containing q.

$$\left(1-r\right)q=-r$$

Divide both sides by 1-r.

$$\frac{\left(1-r\right)q}{1-r}=-\frac{r}{1-r}$$

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

$$q=-\frac{r}{1-r}$$

Variable q cannot be equal to 0.

$$q=-\frac{r}{1-r}\text{, }q\neq 0$$

Solve for r

$$r=-\frac{q}{1-q}$$

$$q\neq 0\text{ and }q\neq 1$$

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 qr, the least common multiple of r,q.

$$q+r=qr$$

Subtract qr from both sides.

$$q+r-qr=0$$

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

$$r-qr=-q$$

Combine all terms containing r.

$$\left(1-q\right)r=-q$$

Divide both sides by 1-q.

$$\frac{\left(1-q\right)r}{1-q}=-\frac{q}{1-q}$$

Dividing by 1-q undoes the multiplication by 1-q.

$$r=-\frac{q}{1-q}$$

Variable r cannot be equal to 0.

$$r=-\frac{q}{1-q}\text{, }r\neq 0$$