Solve 27/a^3-1/27b^3

$$\frac { 27 } { a ^ { 3 } } - \frac { 1 } { 27 b ^ { 3 } }$$

Evaluate

$$\frac{729b^{3}-a^{3}}{27\left(ab\right)^{3}}$$

Short Solution Steps

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

$$\frac{27\times 27b^{3}}{27a^{3}b^{3}}-\frac{a^{3}}{27a^{3}b^{3}}$$

Since \frac{27\times 27b^{3}}{27a^{3}b^{3}} and \frac{a^{3}}{27a^{3}b^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27\times 27b^{3}-a^{3}}{27a^{3}b^{3}}$$

Do the multiplications in 27\times 27b^{3}-a^{3}.

$$\frac{729b^{3}-a^{3}}{27a^{3}b^{3}}$$

Factor

$$\frac{\frac{729b^{3}}{a^{3}}-1}{27b^{3}}$$