Solve 2019^2-1999^2/(1999-2019)^2

$$\frac { 2019 ^ { 2 } - 1999 ^ { 2 } } { ( 1999 - 2019 ) ^ { 2 } }$$

Evaluate

$$\frac{2009}{10}=200.9$$

Solution Steps

Calculate 2019 to the power of 2 and get 4076361.

$$\frac{4076361-1999^{2}}{\left(1999-2019\right)^{2}}$$

Calculate 1999 to the power of 2 and get 3996001.

$$\frac{4076361-3996001}{\left(1999-2019\right)^{2}}$$

Subtract 3996001 from 4076361 to get 80360.

$$\frac{80360}{\left(1999-2019\right)^{2}}$$

Subtract 2019 from 1999 to get -20.

$$\frac{80360}{\left(-20\right)^{2}}$$

Calculate -20 to the power of 2 and get 400.

$$\frac{80360}{400}$$

Reduce the fraction \frac{80360}{400} to lowest terms by extracting and canceling out 40.

$$\frac{2009}{10}$$

Factor

$$\frac{7 ^ {2} \cdot 41}{2 \cdot 5} = 200\frac{9}{10} = 200.9$$