Solve 1/alphabeta+1/betagamma+1/gammaalpha=

$$\frac { 1 } { \alpha \beta } + \frac { 1 } { \beta \gamma } + \frac { 1 } { \gamma \alpha } =$$

Evaluate

$$\frac{\alpha +\beta +\gamma }{\alpha \beta \gamma }$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \alpha \beta and \beta \gamma is \alpha \beta \gamma . Multiply \frac{1}{\alpha \beta } times \frac{\gamma }{\gamma }. Multiply \frac{1}{\beta \gamma } times \frac{\alpha }{\alpha }.

$$\frac{\gamma }{\alpha \beta \gamma }+\frac{\alpha }{\alpha \beta \gamma }+\frac{1}{\gamma \alpha }$$

Since \frac{\gamma }{\alpha \beta \gamma } and \frac{\alpha }{\alpha \beta \gamma } have the same denominator, add them by adding their numerators.

$$\frac{\gamma +\alpha }{\alpha \beta \gamma }+\frac{1}{\gamma \alpha }$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \alpha \beta \gamma and \gamma \alpha is \alpha \beta \gamma . Multiply \frac{1}{\gamma \alpha } times \frac{\beta }{\beta }.

$$\frac{\gamma +\alpha }{\alpha \beta \gamma }+\frac{\beta }{\alpha \beta \gamma }$$

Since \frac{\gamma +\alpha }{\alpha \beta \gamma } and \frac{\beta }{\alpha \beta \gamma } have the same denominator, add them by adding their numerators.

$$\frac{\gamma +\alpha +\beta }{\alpha \beta \gamma }$$

Factor

$$\frac{\alpha +\beta +\gamma }{\alpha \beta \gamma }$$