Resolver 100*10^3-0.5176*14.3*500*465/frac{100*10^3*285-0.43*14.3*500*465^2{(0.8-0.5176)*(465-35)}+14.3*500*465}

$$\frac { 100 \times 10 ^ { 3 } - 0.5176 \times 14.3 \times 500 \times 465 } { \frac { 100 \times 10 ^ { 3 } \times 285 - 0.43 \times 14.3 \times 500 \times 465 ^ { 2 } } { ( 0.8 - 0.5176 ) \times ( 465 - 35 ) } + 14.3 \times 500 \times 465 }$$

Calcular

$$\frac{246034984174}{290690900625}\approx 0.846380068$$

Pasos da solución

Calcula 10 á potencia de 3 e obtén 1000.

$$\frac{100\times 1000-0.5176\times 14.3\times 500\times 465}{\frac{100\times 10^{3}\times 285-0.43\times 14.3\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Multiplica 100 e 1000 para obter 100000.

$$\frac{100000-0.5176\times 14.3\times 500\times 465}{\frac{100\times 10^{3}\times 285-0.43\times 14.3\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Multiplica 0.5176 e 14.3 para obter 7.40168.

$$\frac{100000-7.40168\times 500\times 465}{\frac{100\times 10^{3}\times 285-0.43\times 14.3\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Multiplica 7.40168 e 500 para obter 3700.84.

$$\frac{100000-3700.84\times 465}{\frac{100\times 10^{3}\times 285-0.43\times 14.3\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Multiplica 3700.84 e 465 para obter 1720890.6.

$$\frac{100000-1720890.6}{\frac{100\times 10^{3}\times 285-0.43\times 14.3\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Resta 1720890.6 de 100000 para obter -1620890.6.

$$\frac{-1620890.6}{\frac{100\times 10^{3}\times 285-0.43\times 14.3\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Calcula 10 á potencia de 3 e obtén 1000.

$$\frac{-1620890.6}{\frac{100\times 1000\times 285-0.43\times 14.3\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Multiplica 100 e 1000 para obter 100000.

$$\frac{-1620890.6}{\frac{100000\times 285-0.43\times 14.3\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Multiplica 100000 e 285 para obter 28500000.

$$\frac{-1620890.6}{\frac{28500000-0.43\times 14.3\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Multiplica 0.43 e 14.3 para obter 6.149.

$$\frac{-1620890.6}{\frac{28500000-6.149\times 500\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Multiplica 6.149 e 500 para obter 3074.5.

$$\frac{-1620890.6}{\frac{28500000-3074.5\times 465^{2}}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Calcula 465 á potencia de 2 e obtén 216225.

$$\frac{-1620890.6}{\frac{28500000-3074.5\times 216225}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Multiplica 3074.5 e 216225 para obter 664783762.5.

$$\frac{-1620890.6}{\frac{28500000-664783762.5}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Resta 664783762.5 de 28500000 para obter -636283762.5.

$$\frac{-1620890.6}{\frac{-636283762.5}{\left(0.8-0.5176\right)\left(465-35\right)}+14.3\times 500\times 465}$$

Resta 0.5176 de 0.8 para obter 0.2824.

$$\frac{-1620890.6}{\frac{-636283762.5}{0.2824\left(465-35\right)}+14.3\times 500\times 465}$$

Resta 35 de 465 para obter 430.

$$\frac{-1620890.6}{\frac{-636283762.5}{0.2824\times 430}+14.3\times 500\times 465}$$

Multiplica 0.2824 e 430 para obter 121.432.

$$\frac{-1620890.6}{\frac{-636283762.5}{121.432}+14.3\times 500\times 465}$$

Expande \frac{-636283762.5}{121.432} multiplicando o numerador e o denominador por 1000.

$$\frac{-1620890.6}{\frac{-636283762500}{121432}+14.3\times 500\times 465}$$

Reduce a fracción \frac{-636283762500}{121432} a termos máis baixos extraendo e cancelando 4.

$$\frac{-1620890.6}{-\frac{159070940625}{30358}+14.3\times 500\times 465}$$

Multiplica 14.3 e 500 para obter 7150.

$$\frac{-1620890.6}{-\frac{159070940625}{30358}+7150\times 465}$$

Multiplica 7150 e 465 para obter 3324750.

$$\frac{-1620890.6}{-\frac{159070940625}{30358}+3324750}$$

Converter 3324750 á fracción \frac{100932760500}{30358}.

$$\frac{-1620890.6}{-\frac{159070940625}{30358}+\frac{100932760500}{30358}}$$

Dado que -\frac{159070940625}{30358} e \frac{100932760500}{30358} teñen o mesmo denominador, súmaos mediante a suma dos seus numeradores.

$$\frac{-1620890.6}{\frac{-159070940625+100932760500}{30358}}$$

Suma -159070940625 e 100932760500 para obter -58138180125.

$$\frac{-1620890.6}{-\frac{58138180125}{30358}}$$

Divide -1620890.6 entre -\frac{58138180125}{30358} mediante a multiplicación de -1620890.6 polo recíproco de -\frac{58138180125}{30358}.

$$-1620890.6\left(-\frac{30358}{58138180125}\right)$$

Converte o número decimal -1620890.6 á fracción -\frac{16208906}{10}. Reduce a fracción -\frac{16208906}{10} a termos máis baixos extraendo e cancelando 2.

$$-\frac{8104453}{5}\left(-\frac{30358}{58138180125}\right)$$

Multiplica -\frac{8104453}{5} por -\frac{30358}{58138180125} mediante a multiplicación do numerador polo numerador e do denominador polo denominador.

$$\frac{-8104453\left(-30358\right)}{5\times 58138180125}$$

Fai as multiplicacións na fracción \frac{-8104453\left(-30358\right)}{5\times 58138180125}.

$$\frac{246034984174}{290690900625}$$

Factorizar

$$\frac{2 \cdot 43 \cdot 353 \cdot 165397 \cdot 7 ^ {2}}{3 \cdot 155035147 \cdot 5 ^ {4}} = 0.8463800677799423$$