Solve 1/8a^3+8/b^3

$$\frac { 1 } { 8 a ^ { 3 } } + \frac { 8 } { b ^ { 3 } }$$

Evaluate

$$\frac{64a^{3}+b^{3}}{8\left(ab\right)^{3}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8a^{3} and b^{3} is 8a^{3}b^{3}. Multiply \frac{1}{8a^{3}} times \frac{b^{3}}{b^{3}}. Multiply \frac{8}{b^{3}} times \frac{8a^{3}}{8a^{3}}.

$$\frac{b^{3}}{8a^{3}b^{3}}+\frac{8\times 8a^{3}}{8a^{3}b^{3}}$$

Since \frac{b^{3}}{8a^{3}b^{3}} and \frac{8\times 8a^{3}}{8a^{3}b^{3}} have the same denominator, add them by adding their numerators.

$$\frac{b^{3}+8\times 8a^{3}}{8a^{3}b^{3}}$$

Do the multiplications in b^{3}+8\times 8a^{3}.

$$\frac{b^{3}+64a^{3}}{8a^{3}b^{3}}$$

Factor

$$\frac{\frac{64a^{3}}{b^{3}}+1}{8a^{3}}$$