Solve 5x^6/7-9x^3/14

$$\frac { 5 x ^ { 6 } } { 7 } - \frac { 9 x ^ { 3 } } { 14 }$$

Factor

$$\frac{x^{3}\left(10x^{3}-9\right)}{14}$$

Solution Steps

Factor out \frac{1}{14}.

$$\frac{10x^{6}-9x^{3}}{14}$$

Consider 10x^{6}-9x^{3}. Factor out x^{3}.

$$x^{3}\left(10x^{3}-9\right)$$

Rewrite the complete factored expression. Polynomial 10x^{3}-9 is not factored since it does not have any rational roots.

$$\frac{x^{3}\left(10x^{3}-9\right)}{14}$$

Evaluate

$$\frac{5x^{6}}{7}-\frac{9x^{3}}{14}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and 14 is 14. Multiply \frac{5x^{6}}{7} times \frac{2}{2}.

$$\frac{2\times 5x^{6}}{14}-\frac{9x^{3}}{14}$$

Since \frac{2\times 5x^{6}}{14} and \frac{9x^{3}}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 5x^{6}-9x^{3}}{14}$$

Do the multiplications in 2\times 5x^{6}-9x^{3}.

$$\frac{10x^{6}-9x^{3}}{14}$$