Resolver 5752.56+5752.56/{left(frac{1{1+0.06}right)}^1+{left(1/1+0.06right)}^2}

$$\frac{ 5752.56+5752.56 }{ { \left( \frac{ 1 }{ 1+0.06 } \right) }^{ 1 } + { \left( \frac{ 1 }{ 1+0.06 } \right) }^{ 2 } }$$

Calcular

$$\frac{403973526}{64375}\approx 6275.316908738$$

Pasos da solución

Suma 5752.56 e 5752.56 para obter 11505.12.

$$\frac{11505.12}{\left(\frac{1}{1+0.06}\right)^{1}+\left(\frac{1}{1+0.06}\right)^{2}}$$

Suma 1 e 0.06 para obter 1.06.

$$\frac{11505.12}{\left(\frac{1}{1.06}\right)^{1}+\left(\frac{1}{1+0.06}\right)^{2}}$$

Expande \frac{1}{1.06} multiplicando o numerador e o denominador por 100.

$$\frac{11505.12}{\left(\frac{100}{106}\right)^{1}+\left(\frac{1}{1+0.06}\right)^{2}}$$

Reduce a fracción \frac{100}{106} a termos máis baixos extraendo e cancelando 2.

$$\frac{11505.12}{\left(\frac{50}{53}\right)^{1}+\left(\frac{1}{1+0.06}\right)^{2}}$$

Calcula \frac{50}{53} á potencia de 1 e obtén \frac{50}{53}.

$$\frac{11505.12}{\frac{50}{53}+\left(\frac{1}{1+0.06}\right)^{2}}$$

Suma 1 e 0.06 para obter 1.06.

$$\frac{11505.12}{\frac{50}{53}+\left(\frac{1}{1.06}\right)^{2}}$$

Expande \frac{1}{1.06} multiplicando o numerador e o denominador por 100.

$$\frac{11505.12}{\frac{50}{53}+\left(\frac{100}{106}\right)^{2}}$$

Reduce a fracción \frac{100}{106} a termos máis baixos extraendo e cancelando 2.

$$\frac{11505.12}{\frac{50}{53}+\left(\frac{50}{53}\right)^{2}}$$

Calcula \frac{50}{53} á potencia de 2 e obtén \frac{2500}{2809}.

$$\frac{11505.12}{\frac{50}{53}+\frac{2500}{2809}}$$

Suma \frac{50}{53} e \frac{2500}{2809} para obter \frac{5150}{2809}.

$$\frac{11505.12}{\frac{5150}{2809}}$$

Divide 11505.12 entre \frac{5150}{2809} mediante a multiplicación de 11505.12 polo recíproco de \frac{5150}{2809}.

$$11505.12\times \frac{2809}{5150}$$

Multiplica 11505.12 e \frac{2809}{5150} para obter \frac{403973526}{64375}.

$$\frac{403973526}{64375}$$

Factorizar

$$\frac{2 \cdot 3 \cdot 11 \cdot 2179 \cdot 53 ^ {2}}{103 \cdot 5 ^ {4}} = 6275\frac{20401}{64375} = 6275.316908737864$$