Solve 2*1/2^{2-1^{2}}+frac{-1(2^{2}+1^{2})}{(2^{2}-1^{2})^{2}}*0,01+frac{2(2^{2}+1^2)}{(2^2-1^2)^2}*0,03=

$$\frac { 2 \cdot 1 } { 2 ^ { 2 } - 1 ^ { 2 } } + \frac { - 1 ( 2 ^ { 2 } + 1 ^ { 2 } ) } { ( 2 ^ { 2 } - 1 ^ { 2 } ) ^ { 2 } } \cdot 0,01 + \frac { 2 ( 2 ^ { 2 } + 1 ^ { 2 } ) } { ( 2 ^ { 2 } - 1 ^ { 2 } ) ^ { 2 } } \cdot 0,03 =$$

Evaluate

$$\frac{25}{36}\approx 0,694444444$$

Solution Steps

Multiply 2 and 1 to get 2.

$$\frac{2}{2^{2}-1^{2}}+\frac{-\left(2^{2}+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,01+\frac{2\left(2^{2}+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,03$$

Calculate 2 to the power of 2 and get 4.

$$\frac{2}{4-1^{2}}+\frac{-\left(2^{2}+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,01+\frac{2\left(2^{2}+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,03$$

Calculate 1 to the power of 2 and get 1.

$$\frac{2}{4-1}+\frac{-\left(2^{2}+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,01+\frac{2\left(2^{2}+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,03$$

Subtract 1 from 4 to get 3.

$$\frac{2}{3}+\frac{-\left(2^{2}+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,01+\frac{2\left(2^{2}+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,03$$

Calculate 2 to the power of 2 and get 4.

$$\frac{2}{3}+\frac{-\left(4+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,01+\frac{2\left(2^{2}+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,03$$

Calculate 1 to the power of 2 and get 1.

$$\frac{2}{3}+\frac{-\left(4+1\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,01+\frac{2\left(2^{2}+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,03$$

Add 4 and 1 to get 5.

$$\frac{2}{3}+\frac{-5}{\left(2^{2}-1^{2}\right)^{2}}\times 0,01+\frac{2\left(2^{2}+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,03$$

Calculate 2 to the power of 2 and get 4.

$$\frac{2}{3}+\frac{-5}{\left(4-1^{2}\right)^{2}}\times 0,01+\frac{2\left(2^{2}+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,03$$

Calculate 1 to the power of 2 and get 1.

$$\frac{2}{3}+\frac{-5}{\left(4-1\right)^{2}}\times 0,01+\frac{2\left(2^{2}+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,03$$

Subtract 1 from 4 to get 3.

$$\frac{2}{3}+\frac{-5}{3^{2}}\times 0,01+\frac{2\left(2^{2}+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,03$$

Calculate 3 to the power of 2 and get 9.

$$\frac{2}{3}+\frac{-5}{9}\times 0,01+\frac{2\left(2^{2}+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,03$$

Fraction \frac{-5}{9} can be rewritten as -\frac{5}{9} by extracting the negative sign.

$$\frac{2}{3}-\frac{5}{9}\times 0,01+\frac{2\left(2^{2}+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,03$$

Multiply -\frac{5}{9} and 0,01 to get -\frac{1}{180}.

$$\frac{2}{3}-\frac{1}{180}+\frac{2\left(2^{2}+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,03$$

Subtract \frac{1}{180} from \frac{2}{3} to get \frac{119}{180}.

$$\frac{119}{180}+\frac{2\left(2^{2}+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,03$$

Calculate 2 to the power of 2 and get 4.

$$\frac{119}{180}+\frac{2\left(4+1^{2}\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,03$$

Calculate 1 to the power of 2 and get 1.

$$\frac{119}{180}+\frac{2\left(4+1\right)}{\left(2^{2}-1^{2}\right)^{2}}\times 0,03$$

Add 4 and 1 to get 5.

$$\frac{119}{180}+\frac{2\times 5}{\left(2^{2}-1^{2}\right)^{2}}\times 0,03$$

Multiply 2 and 5 to get 10.

$$\frac{119}{180}+\frac{10}{\left(2^{2}-1^{2}\right)^{2}}\times 0,03$$

Calculate 2 to the power of 2 and get 4.

$$\frac{119}{180}+\frac{10}{\left(4-1^{2}\right)^{2}}\times 0,03$$

Calculate 1 to the power of 2 and get 1.

$$\frac{119}{180}+\frac{10}{\left(4-1\right)^{2}}\times 0,03$$

Subtract 1 from 4 to get 3.

$$\frac{119}{180}+\frac{10}{3^{2}}\times 0,03$$

Calculate 3 to the power of 2 and get 9.

$$\frac{119}{180}+\frac{10}{9}\times 0,03$$

Multiply \frac{10}{9} and 0,03 to get \frac{1}{30}.

$$\frac{119}{180}+\frac{1}{30}$$

Add \frac{119}{180} and \frac{1}{30} to get \frac{25}{36}.

$$\frac{25}{36}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {2} \cdot 3 ^ {2}} = 0.6944444444444444$$