Solve x^5/5+x^6/6

$$\frac { x ^ { 5 } } { 5 } + \frac { x ^ { 6 } } { 6 }$$

Evaluate

$$\frac{x^{6}}{6}+\frac{x^{5}}{5}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 6 is 30. Multiply \frac{x^{5}}{5} times \frac{6}{6}. Multiply \frac{x^{6}}{6} times \frac{5}{5}.

$$\frac{6x^{5}}{30}+\frac{5x^{6}}{30}$$

Since \frac{6x^{5}}{30} and \frac{5x^{6}}{30} have the same denominator, add them by adding their numerators.

$$\frac{6x^{5}+5x^{6}}{30}$$

Factor

$$\frac{\left(5x+6\right)x^{5}}{30}$$

Solution Steps

Factor out \frac{1}{30}.

$$\frac{6x^{5}+5x^{6}}{30}$$

Consider 6x^{5}+5x^{6}. Factor out x^{5}.

$$x^{5}\left(6+5x\right)$$

Rewrite the complete factored expression.

$$\frac{x^{5}\left(5x+6\right)}{30}$$