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

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

Calcular

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

Pasos da solución

Multiplica 73 e 98 para obter 7154.

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

Multiplica 52 e 138 para obter 7176.

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

Resta 7176 de 7154 para obter -22.

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

Calcula -22 á potencia de 2 e obtén 484.

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

Multiplica 361 e 484 para obter 174724.

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

Suma 52 e 98 para obter 150.

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

Suma 73 e 52 para obter 125.

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

Multiplica 150 e 125 para obter 18750.

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

Suma 138 e 98 para obter 236.

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

Multiplica 18750 e 236 para obter 4425000.

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

Suma 73 e 138 para obter 211.

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

Multiplica 4425000 e 211 para obter 933675000.

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

Reduce a fracción \frac{174724}{933675000} a termos máis baixos extraendo e cancelando 4.

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

Factorizar

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