Solve 64x^3-27/x^3+80

$$64 x ^ { 3 } - \frac { 27 } { x ^ { 3 } } + 80$$

Evaluate

$$\frac{\left(8x^{3}+5\right)^{2}-52}{x^{3}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 64x^{3}+80 times \frac{x^{3}}{x^{3}}.

$$\frac{\left(64x^{3}+80\right)x^{3}}{x^{3}}-\frac{27}{x^{3}}$$

Since \frac{\left(64x^{3}+80\right)x^{3}}{x^{3}} and \frac{27}{x^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(64x^{3}+80\right)x^{3}-27}{x^{3}}$$

Do the multiplications in \left(64x^{3}+80\right)x^{3}-27.

$$\frac{64x^{6}+80x^{3}-27}{x^{3}}$$

Factor

$$\frac{64\left(x^{3}-\left(-\frac{\sqrt{13}}{4}-\frac{5}{8}\right)\right)\left(x^{3}-\left(\frac{\sqrt{13}}{4}-\frac{5}{8}\right)\right)}{x^{3}}$$