Solve 1/1,3^2-1,3-2/1,3^2-1+1/1,3^2+1,3

$$\frac { 1 } { 1,3 ^ { 2 } - 1,3 } - \frac { 2 } { 1,3 ^ { 2 } - 1 } + \frac { 1 } { 1,3 ^ { 2 } + 1,3 }$$

Evaluate

$$-\frac{731}{31724}\approx -0,023042491$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\frac{1}{1\times 9-1,3}-\frac{2}{1\times 3^{2}-1}+\frac{1}{1\times 3^{2}+1,3}$$

Multiply 1 and 9 to get 9.

$$\frac{1}{9-1,3}-\frac{2}{1\times 3^{2}-1}+\frac{1}{1\times 3^{2}+1,3}$$

Subtract 1,3 from 9 to get 7,7.

$$\frac{1}{7,7}-\frac{2}{1\times 3^{2}-1}+\frac{1}{1\times 3^{2}+1,3}$$

Expand \frac{1}{7,7} by multiplying both numerator and the denominator by 10.

$$\frac{10}{77}-\frac{2}{1\times 3^{2}-1}+\frac{1}{1\times 3^{2}+1,3}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{10}{77}-\frac{2}{1\times 9-1}+\frac{1}{1\times 3^{2}+1,3}$$

Multiply 1 and 9 to get 9.

$$\frac{10}{77}-\frac{2}{9-1}+\frac{1}{1\times 3^{2}+1,3}$$

Subtract 1 from 9 to get 8.

$$\frac{10}{77}-\frac{2}{8}+\frac{1}{1\times 3^{2}+1,3}$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{10}{77}-\frac{1}{4}+\frac{1}{1\times 3^{2}+1,3}$$

Least common multiple of 77 and 4 is 308. Convert \frac{10}{77} and \frac{1}{4} to fractions with denominator 308.

$$\frac{40}{308}-\frac{77}{308}+\frac{1}{1\times 3^{2}+1,3}$$

Since \frac{40}{308} and \frac{77}{308} have the same denominator, subtract them by subtracting their numerators.

$$\frac{40-77}{308}+\frac{1}{1\times 3^{2}+1,3}$$

Subtract 77 from 40 to get -37.

$$-\frac{37}{308}+\frac{1}{1\times 3^{2}+1,3}$$

Calculate 3 to the power of 2 and get 9.

$$-\frac{37}{308}+\frac{1}{1\times 9+1,3}$$

Multiply 1 and 9 to get 9.

$$-\frac{37}{308}+\frac{1}{9+1,3}$$

Add 9 and 1,3 to get 10,3.

$$-\frac{37}{308}+\frac{1}{10,3}$$

Expand \frac{1}{10,3} by multiplying both numerator and the denominator by 10.

$$-\frac{37}{308}+\frac{10}{103}$$

Least common multiple of 308 and 103 is 31724. Convert -\frac{37}{308} and \frac{10}{103} to fractions with denominator 31724.

$$-\frac{3811}{31724}+\frac{3080}{31724}$$

Since -\frac{3811}{31724} and \frac{3080}{31724} have the same denominator, add them by adding their numerators.

$$\frac{-3811+3080}{31724}$$

Add -3811 and 3080 to get -731.

$$-\frac{731}{31724}$$

Factor

$$-\frac{731}{31724} = -0.02304249148909343$$