Solve 361left(73*98-52*138right)^2/left(52+98right)left(73+52right)left(138+98right)left(73+138right)

$$\frac{ 361 { \left(73 \cdot 98-52 \cdot 138 \right) }^{ 2 } }{ \left( 52+98 \right) \left( 73+52 \right) \left( 138+98 \right) \left( 73+138 \right) }$$

Evaluate

$$\frac{43681}{233418750}\approx 0.000187136$$

Solution Steps

Multiply 73 and 98 to get 7154.

$$\frac{361\left(7154-52\times 138\right)^{2}}{\left(52+98\right)\left(73+52\right)\left(138+98\right)\left(73+138\right)}$$

Multiply 52 and 138 to get 7176.

$$\frac{361\left(7154-7176\right)^{2}}{\left(52+98\right)\left(73+52\right)\left(138+98\right)\left(73+138\right)}$$

Subtract 7176 from 7154 to get -22.

$$\frac{361\left(-22\right)^{2}}{\left(52+98\right)\left(73+52\right)\left(138+98\right)\left(73+138\right)}$$

Calculate -22 to the power of 2 and get 484.

$$\frac{361\times 484}{\left(52+98\right)\left(73+52\right)\left(138+98\right)\left(73+138\right)}$$

Multiply 361 and 484 to get 174724.

$$\frac{174724}{\left(52+98\right)\left(73+52\right)\left(138+98\right)\left(73+138\right)}$$

Add 52 and 98 to get 150.

$$\frac{174724}{150\left(73+52\right)\left(138+98\right)\left(73+138\right)}$$

Add 73 and 52 to get 125.

$$\frac{174724}{150\times 125\left(138+98\right)\left(73+138\right)}$$

Multiply 150 and 125 to get 18750.

$$\frac{174724}{18750\left(138+98\right)\left(73+138\right)}$$

Add 138 and 98 to get 236.

$$\frac{174724}{18750\times 236\left(73+138\right)}$$

Multiply 18750 and 236 to get 4425000.

$$\frac{174724}{4425000\left(73+138\right)}$$

Add 73 and 138 to get 211.

$$\frac{174724}{4425000\times 211}$$

Multiply 4425000 and 211 to get 933675000.

$$\frac{174724}{933675000}$$

Reduce the fraction \frac{174724}{933675000} to lowest terms by extracting and canceling out 4.

$$\frac{43681}{233418750}$$

Factor

$$\frac{11 ^ {2} \cdot 19 ^ {2}}{2 \cdot 3 \cdot 5 ^ {5} \cdot 59 \cdot 211} = 0.00018713578065172572$$