Solve 4left(252+248right)^2/(252^2-248^2)left(114^2+{136^2right)}

$$\frac{ 4 { \left(252+248 \right) }^{ 2 } }{ ( { 252 }^{ 2 } - { 248 }^{ 2 } ) \left( { 114 }^{ 2 } + { 136 }^{ 2 } \right) }$$

Evaluate

$$\frac{125}{7873}\approx 0.015877048$$

Solution Steps

Add 252 and 248 to get 500.

$$\frac{4\times 500^{2}}{\left(252^{2}-248^{2}\right)\left(114^{2}+136^{2}\right)}$$

Calculate 500 to the power of 2 and get 250000.

$$\frac{4\times 250000}{\left(252^{2}-248^{2}\right)\left(114^{2}+136^{2}\right)}$$

Multiply 4 and 250000 to get 1000000.

$$\frac{1000000}{\left(252^{2}-248^{2}\right)\left(114^{2}+136^{2}\right)}$$

Calculate 252 to the power of 2 and get 63504.

$$\frac{1000000}{\left(63504-248^{2}\right)\left(114^{2}+136^{2}\right)}$$

Calculate 248 to the power of 2 and get 61504.

$$\frac{1000000}{\left(63504-61504\right)\left(114^{2}+136^{2}\right)}$$

Subtract 61504 from 63504 to get 2000.

$$\frac{1000000}{2000\left(114^{2}+136^{2}\right)}$$

Calculate 114 to the power of 2 and get 12996.

$$\frac{1000000}{2000\left(12996+136^{2}\right)}$$

Calculate 136 to the power of 2 and get 18496.

$$\frac{1000000}{2000\left(12996+18496\right)}$$

Add 12996 and 18496 to get 31492.

$$\frac{1000000}{2000\times 31492}$$

Multiply 2000 and 31492 to get 62984000.

$$\frac{1000000}{62984000}$$

Reduce the fraction \frac{1000000}{62984000} to lowest terms by extracting and canceling out 8000.

$$\frac{125}{7873}$$

Factor

$$\frac{5 ^ {3}}{7873} = 0.015877048139209957$$