Solve x^3/64-64/x^7

$$\frac { x ^ { 3 } } { 64 } - \frac { 64 } { x ^ { 7 } }$$

Evaluate

$$\frac{x^{3}}{64}-\frac{64}{x^{7}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 64 and x^{7} is 64x^{7}. Multiply \frac{x^{3}}{64} times \frac{x^{7}}{x^{7}}. Multiply \frac{64}{x^{7}} times \frac{64}{64}.

$$\frac{x^{3}x^{7}}{64x^{7}}-\frac{64\times 64}{64x^{7}}$$

Since \frac{x^{3}x^{7}}{64x^{7}} and \frac{64\times 64}{64x^{7}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{3}x^{7}-64\times 64}{64x^{7}}$$

Do the multiplications in x^{3}x^{7}-64\times 64.

$$\frac{x^{10}-4096}{64x^{7}}$$

Factor

$$\frac{\left(x^{5}-64\right)\left(x^{5}+64\right)}{64x^{7}}$$