Solve 1/gamma=1/p+1/r

$$\frac { 1 } { \gamma } = \frac { 1 } { p } + \frac { 1 } { r }$$

Solve for p

$$p=-\frac{r\gamma }{\gamma -r}$$

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

Steps for Solving Linear Equation

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

$$pr=r\gamma +p\gamma$$

Subtract p\gamma from both sides.

$$pr-p\gamma =r\gamma$$

Combine all terms containing p.

$$\left(r-\gamma \right)p=r\gamma$$

Divide both sides by r-\gamma .

$$\frac{\left(r-\gamma \right)p}{r-\gamma }=\frac{r\gamma }{r-\gamma }$$

Dividing by r-\gamma undoes the multiplication by r-\gamma .

$$p=\frac{r\gamma }{r-\gamma }$$

Variable p cannot be equal to 0.

$$p=\frac{r\gamma }{r-\gamma }\text{, }p\neq 0$$

Solve for r

$$r=-\frac{p\gamma }{\gamma -p}$$

$$p\neq 0\text{ and }\gamma \neq 0\text{ and }\gamma \neq p$$

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 pr\gamma , the least common multiple of \gamma ,p,r.

$$pr=r\gamma +p\gamma$$

Subtract r\gamma from both sides.

$$pr-r\gamma =p\gamma$$

Combine all terms containing r.

$$\left(p-\gamma \right)r=p\gamma$$

Divide both sides by p-\gamma .

$$\frac{\left(p-\gamma \right)r}{p-\gamma }=\frac{p\gamma }{p-\gamma }$$

Dividing by p-\gamma undoes the multiplication by p-\gamma .

$$r=\frac{p\gamma }{p-\gamma }$$

Variable r cannot be equal to 0.

$$r=\frac{p\gamma }{p-\gamma }\text{, }r\neq 0$$