Solve 1/b=1/r+1/q

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

Solve for b

$$b=\frac{qr}{q+r}$$

$$q\neq 0\text{ and }r\neq 0\text{ and }r\neq -q$$

Steps for Solving Linear Equation

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

$$qr=bq+br$$

Swap sides so that all variable terms are on the left hand side.

$$bq+br=qr$$

Combine all terms containing b.

$$\left(q+r\right)b=qr$$

Divide both sides by q+r.

$$\frac{\left(q+r\right)b}{q+r}=\frac{qr}{q+r}$$

Dividing by q+r undoes the multiplication by q+r.

$$b=\frac{qr}{q+r}$$

Variable b cannot be equal to 0.

$$b=\frac{qr}{q+r}\text{, }b\neq 0$$

Solve for q

$$q=-\frac{br}{b-r}$$

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

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 bqr, the least common multiple of b,r,q.

$$qr=bq+br$$

Subtract bq from both sides.

$$qr-bq=br$$

Combine all terms containing q.

$$\left(r-b\right)q=br$$

Divide both sides by r-b.

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

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

$$q=\frac{br}{r-b}$$

Variable q cannot be equal to 0.

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