Solve 81*19*(19/81-81/19)/81^2-81*38+19^2

$$\frac { 81 \times 19 \times ( \frac { 19 } { 81 } - \frac { 81 } { 19 } ) } { 81 ^ { 2 } - 81 \times 38 + 19 ^ { 2 } }$$

Evaluate

$$-\frac{50}{31}\approx -1.612903226$$

Solution Steps

Multiply 81 and 19 to get 1539.

$$\frac{1539\left(\frac{19}{81}-\frac{81}{19}\right)}{81^{2}-81\times 38+19^{2}}$$

Least common multiple of 81 and 19 is 1539. Convert \frac{19}{81} and \frac{81}{19} to fractions with denominator 1539.

$$\frac{1539\left(\frac{361}{1539}-\frac{6561}{1539}\right)}{81^{2}-81\times 38+19^{2}}$$

Since \frac{361}{1539} and \frac{6561}{1539} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1539\times \frac{361-6561}{1539}}{81^{2}-81\times 38+19^{2}}$$

Subtract 6561 from 361 to get -6200.

$$\frac{1539\left(-\frac{6200}{1539}\right)}{81^{2}-81\times 38+19^{2}}$$

Cancel out 1539 and 1539.

$$\frac{-6200}{81^{2}-81\times 38+19^{2}}$$

Calculate 81 to the power of 2 and get 6561.

$$\frac{-6200}{6561-81\times 38+19^{2}}$$

Multiply 81 and 38 to get 3078.

$$\frac{-6200}{6561-3078+19^{2}}$$

Subtract 3078 from 6561 to get 3483.

$$\frac{-6200}{3483+19^{2}}$$

Calculate 19 to the power of 2 and get 361.

$$\frac{-6200}{3483+361}$$

Add 3483 and 361 to get 3844.

$$\frac{-6200}{3844}$$

Reduce the fraction \frac{-6200}{3844} to lowest terms by extracting and canceling out 124.

$$-\frac{50}{31}$$

Factor

$$-\frac{50}{31} = -1\frac{19}{31} = -1.6129032258064515$$