Solve x/5+x^3/2=

$$\frac { x } { 5 } + \frac { x ^ { 3 } } { 2 } =$$

Evaluate

$$\frac{x^{3}}{2}+\frac{x}{5}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 2 is 10. Multiply \frac{x}{5} times \frac{2}{2}. Multiply \frac{x^{3}}{2} times \frac{5}{5}.

$$\frac{2x}{10}+\frac{5x^{3}}{10}$$

Since \frac{2x}{10} and \frac{5x^{3}}{10} have the same denominator, add them by adding their numerators.

$$\frac{2x+5x^{3}}{10}$$

Factor

$$\frac{x\left(5x^{2}+2\right)}{10}$$

Solution Steps

Factor out \frac{1}{10}.

$$\frac{2x+5x^{3}}{10}$$

Consider 2x+5x^{3}. Factor out x.

$$x\left(2+5x^{2}\right)$$

Rewrite the complete factored expression. Polynomial 2+5x^{2} is not factored since it does not have any rational roots.

$$\frac{x\left(2+5x^{2}\right)}{10}$$