Solve 1/1728*(1/a^12)-(1/b^6)

$$\frac { 1 } { 1728 } \cdot ( \frac { 1 } { a ^ { 12 } } ) - ( \frac { 1 } { b ^ { 6 } } )$$

Evaluate

$$-\frac{1}{b^{6}}+\frac{1}{1728a^{12}}$$

Short Solution Steps

Multiply \frac{1}{1728} times \frac{1}{a^{12}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{1728a^{12}}-\frac{1}{b^{6}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 1728a^{12} and b^{6} is 1728b^{6}a^{12}. Multiply \frac{1}{1728a^{12}} times \frac{b^{6}}{b^{6}}. Multiply \frac{1}{b^{6}} times \frac{1728a^{12}}{1728a^{12}}.

$$\frac{b^{6}}{1728b^{6}a^{12}}-\frac{1728a^{12}}{1728b^{6}a^{12}}$$

Since \frac{b^{6}}{1728b^{6}a^{12}} and \frac{1728a^{12}}{1728b^{6}a^{12}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{b^{6}-1728a^{12}}{1728b^{6}a^{12}}$$

Factor

$$\frac{-1728+\frac{b^{6}}{a^{12}}}{1728b^{6}}$$