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

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

Evaluate

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

Solution Steps

Add 5752.56 and 5752.56 to get 11505.12.

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

Add 1 and 0.06 to get 1.06.

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

Expand \frac{1}{1.06} by multiplying both numerator and the denominator by 100.

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

Reduce the fraction \frac{100}{106} to lowest terms by extracting and canceling out 2.

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

Calculate \frac{50}{53} to the power of 1 and get \frac{50}{53}.

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

Add 1 and 0.06 to get 1.06.

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

Expand \frac{1}{1.06} by multiplying both numerator and the denominator by 100.

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

Reduce the fraction \frac{100}{106} to lowest terms by extracting and canceling out 2.

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

Calculate \frac{50}{53} to the power of 2 and get \frac{2500}{2809}.

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

Add \frac{50}{53} and \frac{2500}{2809} to get \frac{5150}{2809}.

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

Divide 11505.12 by \frac{5150}{2809} by multiplying 11505.12 by the reciprocal of \frac{5150}{2809}.

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

Multiply 11505.12 and \frac{2809}{5150} to get \frac{403973526}{64375}.

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

Factor

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