Solve a^3+1/a^3+26/27

$$a ^ { 3 } + \frac { 1 } { a ^ { 3 } } + \frac { 26 } { 27 }$$

Evaluate

$$a^{3}+\frac{26}{27}+\frac{1}{a^{3}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a^{3} and 27 is 27a^{3}. Multiply \frac{1}{a^{3}} times \frac{27}{27}. Multiply \frac{26}{27} times \frac{a^{3}}{a^{3}}.

$$a^{3}+\frac{27}{27a^{3}}+\frac{26a^{3}}{27a^{3}}$$

Since \frac{27}{27a^{3}} and \frac{26a^{3}}{27a^{3}} have the same denominator, add them by adding their numerators.

$$a^{3}+\frac{27+26a^{3}}{27a^{3}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply a^{3} times \frac{27a^{3}}{27a^{3}}.

$$\frac{a^{3}\times 27a^{3}}{27a^{3}}+\frac{27+26a^{3}}{27a^{3}}$$

Since \frac{a^{3}\times 27a^{3}}{27a^{3}} and \frac{27+26a^{3}}{27a^{3}} have the same denominator, add them by adding their numerators.

$$\frac{a^{3}\times 27a^{3}+27+26a^{3}}{27a^{3}}$$

Do the multiplications in a^{3}\times 27a^{3}+27+26a^{3}.

$$\frac{27a^{6}+27+26a^{3}}{27a^{3}}$$

Factor

$$\frac{\left(3a^{2}-a+3\right)\left(9a^{4}+3a^{3}-8a^{2}+3a+9\right)}{27a^{3}}$$