Solve 1/alpha^3+1/beta^3

$$\frac { 1 } { \alpha ^ { 3 } } + \frac { 1 } { \beta ^ { 3 } }$$

Evaluate

$$\frac{\alpha ^{3}+\beta ^{3}}{\left(\alpha \beta \right)^{3}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \alpha ^{3} and \beta ^{3} is \alpha ^{3}\beta ^{3}. Multiply \frac{1}{\alpha ^{3}} times \frac{\beta ^{3}}{\beta ^{3}}. Multiply \frac{1}{\beta ^{3}} times \frac{\alpha ^{3}}{\alpha ^{3}}.

$$\frac{\beta ^{3}}{\alpha ^{3}\beta ^{3}}+\frac{\alpha ^{3}}{\alpha ^{3}\beta ^{3}}$$

Since \frac{\beta ^{3}}{\alpha ^{3}\beta ^{3}} and \frac{\alpha ^{3}}{\alpha ^{3}\beta ^{3}} have the same denominator, add them by adding their numerators.

$$\frac{\beta ^{3}+\alpha ^{3}}{\alpha ^{3}\beta ^{3}}$$

Factor

$$\frac{\frac{\alpha ^{3}}{\beta ^{3}}+1}{\alpha ^{3}}$$