Solve (12/13)^2-(1/43)^2

$$( \frac { 12 } { 13 } ) ^ { 2 } - ( \frac { 1 } { 43 } ) ^ { 2 }$$

Evaluate

$$\frac{266087}{312481}\approx 0.851530173$$

Solution Steps

Calculate \frac{12}{13} to the power of 2 and get \frac{144}{169}.

$$\frac{144}{169}-\left(\frac{1}{43}\right)^{2}$$

Calculate \frac{1}{43} to the power of 2 and get \frac{1}{1849}.

$$\frac{144}{169}-\frac{1}{1849}$$

Least common multiple of 169 and 1849 is 312481. Convert \frac{144}{169} and \frac{1}{1849} to fractions with denominator 312481.

$$\frac{266256}{312481}-\frac{169}{312481}$$

Since \frac{266256}{312481} and \frac{169}{312481} have the same denominator, subtract them by subtracting their numerators.

$$\frac{266256-169}{312481}$$

Subtract 169 from 266256 to get 266087.

$$\frac{266087}{312481}$$

Factor

$$\frac{23 ^ {2} \cdot 503}{13 ^ {2} \cdot 43 ^ {2}} = 0.8515301730345205$$