Solve {left(1/6right)}^2-{left(1/7right)}^2

$${ \left( \frac{ 1 }{ 6 } \right) }^{ 2 } - { \left( \frac{ 1 }{ 7 } \right) }^{ 2 }$$

Evaluate

$$\frac{13}{1764}\approx 0.007369615$$

Solution Steps

Calculate \frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$\frac{1}{36}-\left(\frac{1}{7}\right)^{2}$$

Calculate \frac{1}{7} to the power of 2 and get \frac{1}{49}.

$$\frac{1}{36}-\frac{1}{49}$$

Least common multiple of 36 and 49 is 1764. Convert \frac{1}{36} and \frac{1}{49} to fractions with denominator 1764.

$$\frac{49}{1764}-\frac{36}{1764}$$

Since \frac{49}{1764} and \frac{36}{1764} have the same denominator, subtract them by subtracting their numerators.

$$\frac{49-36}{1764}$$

Subtract 36 from 49 to get 13.

$$\frac{13}{1764}$$

Factor

$$\frac{13}{2 ^ {2} \cdot 3 ^ {2} \cdot 7 ^ {2}} = 0.007369614512471655$$