Solve (0.996/1+0.996)^2(101.3/100)^2/(frac{1-0.996{1+0.996})*(101.3/100)}

$$\frac { ( \frac { 0.996 } { 1 + 0.996 } ) ^ { 2 } ( \frac { 101.3 } { 100 } ) ^ { 2 } } { ( \frac { 1 - 0.996 } { 1 + 0.996 } ) \times ( \frac { 101.3 } { 100 } ) }$$

Evaluate

$$\frac{62807013}{499000}\approx 125.865757515$$

Solution Steps

Add 1 and 0.996 to get 1.996.

$$\frac{\left(\frac{0.996}{1.996}\right)^{2}\times \left(\frac{101.3}{100}\right)^{2}}{\frac{1-0.996}{1+0.996}\times \frac{101.3}{100}}$$

Expand \frac{0.996}{1.996} by multiplying both numerator and the denominator by 1000.

$$\frac{\left(\frac{996}{1996}\right)^{2}\times \left(\frac{101.3}{100}\right)^{2}}{\frac{1-0.996}{1+0.996}\times \frac{101.3}{100}}$$

Reduce the fraction \frac{996}{1996} to lowest terms by extracting and canceling out 4.

$$\frac{\left(\frac{249}{499}\right)^{2}\times \left(\frac{101.3}{100}\right)^{2}}{\frac{1-0.996}{1+0.996}\times \frac{101.3}{100}}$$

Calculate \frac{249}{499} to the power of 2 and get \frac{62001}{249001}.

$$\frac{\frac{62001}{249001}\times \left(\frac{101.3}{100}\right)^{2}}{\frac{1-0.996}{1+0.996}\times \frac{101.3}{100}}$$

Expand \frac{101.3}{100} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{62001}{249001}\times \left(\frac{1013}{1000}\right)^{2}}{\frac{1-0.996}{1+0.996}\times \frac{101.3}{100}}$$

Calculate \frac{1013}{1000} to the power of 2 and get \frac{1026169}{1000000}.

$$\frac{\frac{62001}{249001}\times \frac{1026169}{1000000}}{\frac{1-0.996}{1+0.996}\times \frac{101.3}{100}}$$

Multiply \frac{62001}{249001} and \frac{1026169}{1000000} to get \frac{63623504169}{249001000000}.

$$\frac{\frac{63623504169}{249001000000}}{\frac{1-0.996}{1+0.996}\times \frac{101.3}{100}}$$

Subtract 0.996 from 1 to get 0.004.

$$\frac{\frac{63623504169}{249001000000}}{\frac{0.004}{1+0.996}\times \frac{101.3}{100}}$$

Add 1 and 0.996 to get 1.996.

$$\frac{\frac{63623504169}{249001000000}}{\frac{0.004}{1.996}\times \frac{101.3}{100}}$$

Expand \frac{0.004}{1.996} by multiplying both numerator and the denominator by 1000.

$$\frac{\frac{63623504169}{249001000000}}{\frac{4}{1996}\times \frac{101.3}{100}}$$

Reduce the fraction \frac{4}{1996} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{63623504169}{249001000000}}{\frac{1}{499}\times \frac{101.3}{100}}$$

Expand \frac{101.3}{100} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{63623504169}{249001000000}}{\frac{1}{499}\times \frac{1013}{1000}}$$

Multiply \frac{1}{499} and \frac{1013}{1000} to get \frac{1013}{499000}.

$$\frac{\frac{63623504169}{249001000000}}{\frac{1013}{499000}}$$

Divide \frac{63623504169}{249001000000} by \frac{1013}{499000} by multiplying \frac{63623504169}{249001000000} by the reciprocal of \frac{1013}{499000}.

$$\frac{63623504169}{249001000000}\times \frac{499000}{1013}$$

Multiply \frac{63623504169}{249001000000} and \frac{499000}{1013} to get \frac{62807013}{499000}.

$$\frac{62807013}{499000}$$

Factor

$$\frac{1013 \cdot 3 ^ {2} \cdot 83 ^ {2}}{499 \cdot 2 ^ {3} \cdot 5 ^ {3}} = 125\frac{432013}{499000} = 125.86575751503005$$